what would be the right thing to do in that scenario. Convert the calls at the option price to get the CVRs or just sell thro options and be done?
Depends if YOU want to be done or not. First...you'd need to have the cash to convert the calls at your strike price. You may have other needs for that cash. The call price itself might include some value reflective of the CVR, but probably much less than the dollar value of the CVR since the CVR covers something in the future....possibly waaay in the future, plus there's no guarantee the acquiring company will hit the target that triggers the CVR.
Also - is it the same concept if the BO would be for cash + a share of stock?
No. A B/O of cash and stock is not equivalent to a CVR. You get cash...and stock, which you could then sell anytime you wish.