You shouldn't worry about stressing him out by feeding if you give him proper time to adjust to his new environment.
Leave him alone for a week before attempting to feed him. Spot clean and change water normally, but do not handle or touch him during this adjustment week.

And as for 7 inch tub side, that's is plenty tall. I've successfully fed snakes in shorter tubs. Don't worry if he tries to strike out. Just gently push him back into the tub if he's hanging out.
If you really want to put the tub lid back on, just cover part of the tub so you can still monitor the feeding.