On the TT trainer just take it off!!
I re-maidenned my Skyvista about three weeks ago(now ti will belong to my son) and was flying it wothout cowling since u havent had it painted yet.
Saturday I put it on and we went flying yesterday .. noo problems!!!
In most trainers the cowling is either plastic or fiberglass reinforced plastic very light weight it would not affect the CG considewrably if anything. On a bigger heavier model YES recheck the CG.. a friend has a 1/3 scale sopwith pup.. the xowling on that puppy is about 1 lb!!!
For your trainer ot won't mess anything (or rather the plane won't miss it