You can totally do this and it is not weird to not want to piss all over yourself. Is it for everyone, nope. I personally did this for a couple of reasons.
1. I didn't like pissing all over myself.
2. I liked being able to pee if needed with ease while on a boat surf surface interval. Most boats do not want you in the "dry" area with your wetsuit on. They want you DRY, but that is also where the head is.
I got some tubing from Home Depot. It was the clear flexible rubbery type tubing about the same size as ice maker tubing. The tubing is flexible but stiff enough to not collapse under the wetsuit. I then got a short piece of the same style tubing that had an inside diameter the same as the outside diameter of the main pee tube. This allowed me to make a "plug" about an inch long that fits a condom cath. When I wear a wetsuit, I also wear a lycra suit underneath as it helps get the wetsuit on. This also plays a part in getting my "pee tube" installed. I simply stick the pee tube in my left leg of the lycra suit and make sure some of the tube is sticking out the bottom of the leg. Then I slide my lycra suit on and then attach the tube to my cath and zip my lycra up the rest of the way. At this point I can "adjust" the tube to sit on the inside of my left leg under the lycra. When I slip my wetsuit on the tube does not move at all. I then put my booties on and the tube is on outside of my boot and I roll down my wetsuit leg on the outside of my bootie. When just standing there you would never know I have about an inch of tubing hanging out the bottom of my wetsuit. When I got to pee while on a boat, I simply hang my left foot over the side.
PS. Clean the wetsuit tube the same as you would a drysuit pee valve tube. A good steramine flush and you are good to go.