OM10's were my front line cameras for a decade; they had the wonderful property of often being cheaper than a roll of decent film!
I killed a couple of them.. through pure abuse or accident, and one sat infront of me on the record-player is rather battered.. top plate is cracked, the auto-manual/test switch a bit cantankerous, after being dropped off a castle wall when bunted by a tear-away child! B-U-T... still takes pictures, so what the heck!
It was 'superseded' by an OM4, circa 1995, but then I kept returning to the thing as it usually had batteries that weren't 'flat' in it! lol! So it has remained,.. If it aint broke... don't fix it! Oh-Kay.. so it's 'sort' of broke... but still don't really need 'fixing' ..I probably would have bought another, b-u-t, always seemed a waste of money, even at the pocket money prces of 'tens' to invest in a system I had wanted to move away from.. so I still have and still occassionally use the battered ten!
I did make a Franken-Camera out of the first two to get damaged, when I was still at uni and funds tighter, but I have to say that they are a bit fiddly, when opened, and for what they cost, it 'probably' isn't worth the effort... if you have the manual adapter, rob that off, and buy another body! Quarter century ago, there were so many that had been bought for a summer holiday, pampered as precious icons in the original box between outings in which they probably never exposed more than 100 frames, to end up traded in for 'autro-focus' wonder-busses, when they came along, or more often simpler compacts the owner might be more inclined to use, they seldom commanded much more than a tenner in the second hand shops, who usually had two or three of them to choose from!
Under the bottom plate, from memory are a few cogs for the accessory winder mechanism, some circuitry including the contacts for the shutter release of a wider, but not a lot else, ad I have an incling that the battery compartment cover actually screws into the battery charger 'through' the bottom plate, not to the bottom plate itself.
IF the camera 'works' as configured, I would leave it alone and just use it. It's unlikely there is any damage that would impair functionality, though possible that if you fitted a winder, may reveal that gear train is out of align or remote shutter release not so well connected, but you don't 'need' to use winder! So, just ignore, and use and enjoy. They are a fantastic camera for the cash, and can take a remarkable amount of battering before they actually stop working..... unlike an OM4, which doesn't need ANY battering to stop working.. They just need batteries... lots and lots of batteries! lol!