Lol we may never know for sure till we get there (actually, make that a "probably won't" rather than a "may never")! It is actually quite interesting that we have three different sides of interpretation as opposed to just two on this particular phrase, and the vulgate using "ambidextrous" may shed some light as to why the Catholics held their weird anti-lefty thing for so long.The idea that his right hand was crippled makes a lot of sense in the case of Ehud, as you have outlined. Interestingly the Geneva bible translated this as "a man lame of his right hande".
However, the idea that the tribe of Benjamin would have 700 men who all coincidentally happened to have crippled right hands so had all trained as left-handed slingers stretches credibility. Maybe it was a possibility that everyone who happened to get a right-hand injury were all trained as slingers, and such injuries were common in that tribe for some reason? It's a long shot.
So I looked at the LXX and (out of pure curiosity, not to find an authoritative answer) the Vulgate (well, English translations of both). The LXX and Vulgate both state that Ehud was ambidextrous - "used the left hand as well as the right". And with regard to the slingers, the LXX just says they were left-handed, but the Vulgate states that they were ambidextrous. Ambidextrous slingers make enormous sense militarily. Imagine training to use the sword well with the right hand and the sling well with the left - such a man would be a formidable warrior, while being very lightly equipped and fast on his feet.
I don't know what the answer is here - any of these options makes a lot of practical sense for different reasons. But the idea that Ehud was a cripple is very compelling.
As for there being 700 cripples, I agree that it doesn't really make contextual sense apart from that they used slings and no other weapon is mentioned for these particular guys. Likewise, any reason as to why there would be 700 crippled warriors is not stated. We could speculate, it could've been some birth defect common in the tribe of Benjamin, maybe some localized areas started to cut off hands as a legal punishment, perhaps one of Israel's oppressors tried to curb rebellion by crippling the men's fighting hands, but any reason we could come up with would be pure speculation and not something we should teach as anything but.
However, in the potential case of having a bunch of one-handed cripples, I don't think it is entirely unreasonable that they would all learn how to use slings. Really, once one guy started doing that, I could see the rest following suit. It would be a way to still be useful as a warrior even with such disability. Likewise, if they could indeed hit a hair's breadth, they could even hunt birds with some degree of reliability, so you could still have some good use outside of battle too. Either way though, whether ambidextrous or one-handedness, it's at least making the best use of the talents and tools that you've got!
Although I will definitely agree wholeheartedly ----- an ambidextrous swordsman slinger would be absolutely terrifying to face in battle!