Anything with spikes is more likely to damage them. I just used cheap tennis shoes.
It's more about how you walk/stand. Try to stay up on the ball of your foot to maximize weight on a smaller area. Increases the friction.
Also I frequently had 2 pairs of shoes. One pair to walk around the job with, another that I'd put on at the ladder. Keeping the roof pair clean and dry.
Korker overshoes work just fine. Tuck loose straps so you don't trip. You're smart for not going off half-cocked and stepping off the ladder on a slick roof. That sort of thing has retired many a young man... either on permanent t disability or the grave.
Don't. Do. It. (Without adequate fall protection in place.) 30-some years ago I had a super close call that would have probably resulted in my demise with a shake roof. I slid from the peak (standing erect) to about eight inches from the eave before something miraculously stopped me from falling more than 25 feet onto a concrete pad. I still have nightmares from that f'ing day.