Yes,
Sneak of Shadows increases as your level does. Taking a multiclass feat gives you the full rights and privileges of whatever you qualify for in regards to the additional class.
In this case Sneak of Shadows grants you the ability to use Sneak Attack 1/encounter as a rogue of your level.
Problem?
In this particular case, nothing. Any concern you might have about "overpowered" is mitigated by his stats being at unimpressive levels. From your previous question you indicate that the players are not leaning toward min-max, power gaming, nor optimization in a munchkinny way. He's using finesse weapons that in time may limit highest damage potential: but if they aren't in min max mode, that does not seem to matter to the group.
At higher levels, he may get a little frustrated with melee damage since there are no two-handed finesse weapons and there are fewer choices in weapons ... but a lot of that gets into what fighting styles he uses and chooses. (And you control what magical weapons, if any, become available so you can tailor that to this party/team. Our DM did just that for our Bard, who is a rapier using singer).
At higher levels he'll benefit from those Divine Smite nova shots. When paired with sneak attacks from his rogue levels, he should be able to keep his damage in a "good enough" zone if the party fights well as a team.
The other place a low Strength would be a Paladin issue is in armor selection: if he wants Chain, Splint or Plate, he needs 13 / 15 / 15 strength respectively. With the proposed Dex build and Rogue multiclass, he's unlikely to want them since they give Disadvantage on Stealth checks. He can wear Breastplate with no minimum Strength requirement -- allows up to +2 of his Dex AC bonus, and no disadvantage for stealth. At 400 GP it may be a level or two before he can afford it. A 50 GP chain shirt may be his best for the time being.
From @Ethan's comment: With leather armor, a shield, and 20 Dex (After a ASI's) he will end up with 19 AC, 1 lower than full plate+shield, but the Piradin will be good at all +Dex skills. This makes for solid function when full plate isn't a good idea -- such as waterborne adventures. His damage output will be identical to a strength based shield using paladin (barring difference in MC class features).
If this is a role and story based move, all the more reason to go with it. It sounds like fun - which is why we play. As long as the player knows where the difficulties are up front with the stats as is, the player is taking on a challenge. Good on 'em!
I'd recommend a ruling to let him proceed as desired. (And if later on they finds some gauntlets of ogre strength ... )
Best Answer
Craven is a great damage boost to a sneak attacker, especially one that is behind a single-classed rogue in sneak attack damage dice. A single-classed rogue expects approximately 1¾ damage/level from sneak attack. Craven boosts that to 2¾, which is +60% damage, and it scales on character level, so the boost is easily double or more for a multiclassed rogue (in the extreme case, 1d6 sneak attack damage, the boost is nearly 6×).
Certainly, 1d6 damage is not significant at 20th level (or indeed, at many levels prior to that point), while 1d6+20 damage is (or at least is more so, as long as you’re making enough attacks). But context is crucial here: how much damage are you doing otherwise? How many attacks are you making?
If you were a charger without pounce, but with Shock Trooper, Spirited Charge, a lance, et al., you could easily have a single attack dealing upwards of +100 damage at 20th level. Is another +20 on top of that, that also requires you to awkwardly ensure your charge target is eligible for sneak attack, going to make a big difference? No, it is not.
On the other hand, if your build is a hodgepodge of things that gets fifteen attacks, adding +20 to each of them is a big deal, especially since you probably haven’t otherwise scored a lot of damage bonuses in your devotion to simply having more attacks.
Generally speaking, sneak attack is an awkward and difficult form of damage-dealing. Setting it up is difficult and capitalizing on it is arguably more so. That takes a lot of investment, and Craven alone isn’t going to save things if you aren’t in a position to make the most of sneak attack to begin with. And even with that investment, you won’t keep up with dedicated two-handed weapon damage dealers.
Finally, this all assuming we are talking solely about damage. Rogues, particularly multiclass ones, may not care about damage in combat. They may be social characters, mostly ignoring combat, or they may focus on battlefield control or debuffs, or what have you. For such rogues, sneak attack is an incidental feature that doesn’t matter much (and should maybe be replaced with feats).
The last thing to consider is that, in addition to the difficulties that sneak attack itself has, Craven adds a massive drawback—you lose the feat if you are immune to fear. Which also means you lose the feat if you are immune to mind-affecting. And since these immunities are extremely valuable, almost critical, at mid-to-high levels, giving up on them is a really big deal. That alone is a really good reason to question the need to take Craven.
But in the end, if you have your heart set on dealing damage specifically via sneak attack, Craven is too large a damage booster to ignore.