Yes, the Wyvern is probably intended to have disadvantage.
While Word of God could always overturn this (but it didn't), it seems pretty clear that the intent is for this to apply to reach attacks. They have the key phrase "ranged attack" and use it elsewhere in the rules (e.g. in the Monk's deflect arrows ability). This heavily implies that the more awkward wording is there for a reason.
They might have worded it this way so that ranged attacks made from melee are normal, rather than disadvantaged. But I suspect this case is less likely than the reach attack one (your mileage may vary).
In other words, it's not a case where it looks like they used simple language and forgot about some corner cases, like the interaction between druids and lethal damage.
As to why this would be the case, consider that a large wyvern doesn't have a 10' body with a long head that sits 10' away. The entire wyvern occupies a 10'x10' space, and stretches or pounces when it needs to attack outside of reach. This kind of stretching / pouncing will inherently limit the creature's attack vectors, perhaps in a way that dropping to the ground will help.
In other words, the monster isn't right there. The monster is still 10' away.
Also remember that the monster doesn't have to stay at range. As soon as they drop prone, it can close to within 5' and start taking advantage on its attacks.
From a mechanical standpoint, this makes prone a general strategy to take for things attacking you that you can't reach and/or luring things into melee. This simplifies the mechanical design, and helps avoid loopholes.
As a house rule, you can certainly scale down the effectiveness of the prone condition. It's unlikely to break much with the current corpus of monsters. However, doing so will always compete with simply closing to melee and gaining advantage... And it is unlikely that this will be brought into the official rules (although maybe it will! Sloppy templating, etc.).
RAW - No, Otto's Irresistible Dance is not a Charm spell
It does not say that the target will be "charmed", and the condition it imposes is significantly different than the description of the "Charmed" condition.
OID:
A dancing creature must use all its movement to dance without leaving its space and has disadvantage on Dexterity saving throws and attack rolls. While the target is affected by this spell, other creatures have advantage on attack rolls against it.
Charmed:
A charmed creature can't attack the charmer or target the charmer with harmful abilities or magical effects. The charmer has advantage on any ability check to interact socially with the creature.
A dancing creature can attack the caster (with disadvantage -- and that disadvantage applies to any attack, not just against the caster) and can cast AoE spells that include the caster and anyone else they choose in the target area with no penalty. They just can't move freely. A charmed character can move freely but can't attack or target the caster.
Furthermore, if it were a Charm spell, it would not be necessary to specify that "[c]reatures that can't be charmed are immune to this spell." That appears to be listed as a special exception.
RAI - No, Otto's Irresistible Dance does not impose the Charmed condition
Jeremy Crawford has tweeted saying:
Being charmed means being subjected to the charmed condition
Since OID does not impose the Charmed condition, the Fey Ancestry resistance to "being charmed" does not apply.
What makes sense?
Webster's dictionary says:
charm: to affect by or as if by magic : compel
Magically forcing someone to dance seems to fall completely within that definition.
I would give those with Fey Ancestry advantage on saves against all enchantment spells that compel the user to do something that is not their own free choice. This includes many spells that do not specifically say they are "charms" or that they impose the "Charmed" condition, such as command, compelled duel, and yes, Otto's irresistible dance. I believe those all fall within the common sense and dictionary definitions of "charmed" in this context, and there's nothing in the description of Fey Ancestry that says it only applies to things that grant the "Charmed" condition.
Best Answer
GoodSirTheSir has a good response about the mechanics, but if this is something you really want to do then you can use RAW to make it work.
Advantage and Disadvantage
One of the biggest boons for this is that Advantage and Disadvantage do not stack, but instead cancel out.
Basic rules p. 57:
If your spellcaster is blind, they will always have disadvantage on attacks. However, if they find a way to give themselves advantage on the attack (which is pretty easy in 5e with helping, spells, and DM fiat), then the disadvantage goes away and they're back to making regular attack rolls. They will never be able to get advantage on an attack, but spells like Bless can help make up for that. An additional bonus is that as long as they can give themselves advantage in some way, they will never ever be forced to roll attacks at disadvantage.
Unseen Attackers
5e, in my opinion, has very strange rules for unseen attackers. Being unable to see someone seems to have no bearing on whether or not you are aware of their location. Furthermore, there is nothing that states that being unable to see someone has any negative effect on your combat efficacy at all. Other than failing checks that rely on sight (which, other than counting birds a mile away through a plate glass window is 100% up to interpretation and thus DM fiat), you can be blind as a bat and still have perfect situational awareness. In fact, there are some situations where it is easier to detect someone if you can't see them than if you can (passive perception vs active perception for hiding, using the 'Lucky' feat, etc).
Here are the rules for attacking unseen attackers:
This is a very important part. It states that you have disadvantage whether you're guessing the target's location, or whether you can hear but not see them. In your case, you can hear but not see the enemy, so by RAW you don't ever have to guess where they are. You just 'know' their location.
Again, the above rules state this only applies to when you have to guess at the target's location, which is not the case when you can hear the attacker.
So, as long as you can hear the attacker, you always know where they are.
Hiding
The biggest downside I can determine is that if you're blind, anyone can hide from you at any time as a standard action. Basically, you're granting the enemies permanent invisibility:
If you're facing smart enemies, they will realize this eventually and make stealth checks even when they're standing next to you. If you fail the perception check to detect them, they are now 'hidden', and according to the rules that means that you no longer know their location (and would thus be beholden to the 'attacking unseen targets' rule above).
So, if you concentrate on giving yourself advantage, and giving your enemies disadvantage, you'll have almost the same efficacy as if you were never blind in the first place.