Ideally he should not be washed until the stitches come out but if it becomes vital you can cover the area including the stitches with Vaseline and that will waterproof the stitches.
I know it awful when they smell but another short term option is to wipe him down all over with Baby Wipes, this will help.
You can also sponge bath the main parts with warm to hot water a tiny amount of shampoo and squeeze sponge tight and wipe all over.
There are also dry shampoos for dogs but I don’t know how good they are.
If he is nervous it would be best for you to start this cleaning, washing procedure at home where he feels safe.
Going to a strange place and all the noisy equipment would not help his disposition at the moment.
Good Luck.