To answer your question directly:
No, making this change would not be game breaking
This would impact the damage done by certain character builds - that is true. It very well may make certain character build less fun (like a strength based rogue).
Game breaking is a strong phrase. I don't believe that making this change (or not) would have that big of an impact to a campaign. Campaigns with Barbarian/Rogues can exist with no changes. Campaigns without a Barbarian/Rogue can exist as well.
A question that you really want to answer is: what mechanical problem you are solving by changing the mechanics of how abilities function?
This proposed change would impact strength based rogues. Some players find that in combat, more damage is fun. If you have a player like that in your group, playing a strength based rogue, this will directly impact how much fun that player can have in combat.
If this seems silly, or doesn't make sense, (but isn't causing mechanical issues) my recommendation would be: resolve that issue without changing the ways abilities work.
I see the hilarity in a barbarian being sneaky while also recklessly attacking. However, I'm very averse to changing abilities or mechanics as substantially as this without a clear mechanical problem that the change would fix.
As much as possible, I try to avoid 'fixing' things that aren't yet causing a problem. If you think this may cause a problem in the future, point that out to your players and make sure they clearly understand that if it becomes a problem, something may have to change.
Would making this change (or not) be game breaking? In and of itself, no.
It very possibly may hurt player fun though.
Best Answer
Try creating it off of a weapon template such as a javelin
I don't think you will be able to create what you want with a shield. However if you made it a weapon template, then added an AC bonus modifier when equipped, it would essentially function as the weaponized shield that you want.
Rename the text of the javelin to be your shield so it shows up how you want it on your character sheet!
I just ran through it real quick on my phone: When using the javelin template, add Modifier Type: Bonus and Modifier Subtype: Armor Class and you can give it the Fixed Value of 2
To add even further to it: In order to make this truly Captain America's shield, you could create a Weapon Bond like the Eldritch Knight gains access to at the 3rd level
So you could essentially throw it as a ranged weapon, have it teleport back into your hand, and still give you the +2 AC for having a shield. It should however be noted that your AC would be -2 once you throw it until it is back into your hand.