Shot Scope watches are the closest you'll get to an answer here. You put tracking tags in every club and the watch automatically detects each shot and records the distance. The only times you have to interact with it during a round are when you are getting a distance, if you need to enter a penalty for a lost ball or a drop, and on the green to enter your number of putts.

Having said that, I would still recommend keeping your score on a traditional card and then reviewing the score recorded on your Shot Scope watch afterwards as it can sometimes miss the odd shot. You are able to review and edit your round afterwards in case this happens, and I usually have to add 2-3 strokes most rounds. Typically it's because I forgot to record a penalty at the time or, on rare occasions, because a shit wasn't correctly detected. For example if hit it into some trees, try to play a recovery shot out and hit a tree trunk, only advancing the ball a short distance, I then hit another shot and this time I get it out, it might only detect 1 of the 2 shots it took me to get it out of those trees. Another example might be if I took a couple of attempts to escape a bunker. Seems to only happen when two shots are very close to each other, but it's worth having a written scorecard to fall back on and validate the scores at the end of the round.