I'm sorry if this has been addressed, but I didn't find an answer.  Is it okay to put the OSMO in the checked bag without any batteries?  I would obviously bring the batteries in my carry on.

the batteries should be small enough to carry on.  

I'd prefer to keep the Osmo in my hand luggage for "safety"......

If you could see how luggage gets thrown around by airport luggage handlers, youd think twice about giving them your delicate OSMO.
I always take ALL cameras in hand luggage.

Yes, in hand luggage definitely but note: make sure you take the camera OUT of the bag at security and place on separate tray so they can clearly see what it is (same as you would with laptop) or you could get held up for ages as i was and nearly missed my flight. Security were very suspicious of my Osmo then put me in queue to have my bag examined thoroughly. Also, note that on some budget flights now, they only let a certain number of bags (the first xxxx) on for hand luggage and tag your bag to go into hold if you haven't paid extra for speedy boarding. Again i had to argue for hours to get my bag (which had several cameras) on with me. Beware of budget airlines and their appalling customer care.