Five years ago, I had right hand trigger thumb release surgery. On March 7th of this year, I had right middle finger trigger release surgery. I am ambidextrous, but left hand dominant. As for your soiled dressing, perhaps you could try wiping at the soiled area with a damp washcloth, but don't let the dressing get soaked through so your stitches won't get wet. As for using your bandaged hand - there is a reason for so much bandaging. It is okay to limit your activities with that hand until the bandage is removed. Yes, the whole business is nerve wracking because we use our hands so much to do so many things. I don't remember any guidelines being given to me after my trigger thumb surgery. I took it easy for about 3-4 days. While my hand was bandaged, I was limited as to what I could do, which was best. The wrapping and padding is there to limit your mobility so you don't rip the stitches and/or hurt the incision. Please have patience. Many years ago, I ripped and tore the tendons in my left thumb and that took a year to heal. I can't use utensils with my right hand easily so was limited to eating sandwiches and finger foods.
Since having the trigger release surgery, I am finding out how difficult it is to open bottles or jars or use scissors. Even though I am left handed, I was raised in a right handed world and cannot use scissors with my left hand. Perhaps you could find some large rubber gloves to put on your right hand to help when you need a little extra assist.