I myself don't wear a belt for anything I do in the gym or events. If I were you, I would start using lighter weights for a set or two of whatever event you are working on without a belt. This would get you conditioned to not using one. Then I would make sure that you tooka heavier set with a belt. Over time I would try to make those lighter sets heavier (still no belt of course). Eventually, I think you could work up to the point of not needing a belt.
For example:
Yoke walk: lets say that 600lbs for 80ft is a big struggle for you.
I would do about 300 or so for a couple sets of 50-80ft no belt
Then maybe go about 450 for 25 ft. no belt
Then take your 600 run with a belt. In addition, you could do a static set with 600 and not use a belt.
These are my ideas, I am not an expert on the subject. I am sure others will pitch in better ideas