I would definitely shave the area, it will grow back. Being a maltipoo he probably has a long coat.
There is an expressing technique called "express, rest, express". You express the bladder, wait 5 minutes (or however long you need to) and then express again. If you wait a few minutes after expressing, the bladder will shrink and regain its round shape and tone, and make it easier for you to express again. You may have to express him more than once to get him empty. With practice your fingers will learn what an empty bladder feels like. I thought I was getting my dog empty the first couple of weeks but I was not.
I would wait till you are outdoors to remove the male wrap and then put it back on before carrying him inside. You could also express him indoors on a puppytraining pad or underpad, do you have any of those? It will save you carrying him outside so often. Hang in there, it gets easier.
There are several formulas of Desitin, I would choose one without zinc oxide. Zinc oxide is poisonous if licked. I tried original formula Desitin with zinc and it did a fantastic job, but got on his fur outside the male wrap somehow (don't ask me
). I'm afraid if that happens to your dog, with a light colored coat you won't be able to see it. My dog is a golden retriever so I could see it. I use A&D original ointment (without zinc) and it does a good job and has a nice manly scent.
I realized the reason my dog got a urine burn was I was not putting on the ointment often enough, because then I had greasy fingers which were hard to wipe and wash off, and it also made putting the male wrap back on hard because I didn't want to smear ointment on the wrap. I solved that problem by getting disposable gloves from Walgreens. I wear them to apply the ointment, then remove them to fasten the wrap.