I'd only wrap with sinew after reaching target weight, otherwise you won't be able to work this area. If you're within 4lb, you'll probably lose that in shooting it in. So its probably time.
And yes you can snakeskin over sinew, in fact it is common to put skins over sinew since they help keep the sinew dry.
I agree with Badger, usually small checks on osage don't cause problems. If it looks like it might grow to an edge, then a wrap would be a preventative measure. Good luck.