Not sure that going to a double crank will eliminate chain rub. Unless you ride in the small rings a lot. And if you do the loosing that gear range will be a problem too. But you'll find out on your own.

As long as the new rings are close to the same sizes that the triple had (mid and large) you'll be fine. There is a chance that the ft der cage inner plate's bottom might contact the double's small ring teeth tops when in the large... There's a chance you might bot find that the triple shifter throws the ft der in a range that a double wants. (Therefore increasing the chance of rub). Switching the shifter to a double would help prevent this. Simple ft der adjusting will be needed, range limits redone and maybe position on the frame with cable tension adjustments.

The best way to eliminate rub is to both have the system well adjusted and then NOT USE the combos that rub. Shimano long ago published a little guide for which combos to not use. As you suspect it said to avoid those combos that did rub badly but that some rub wasn't wrong. Andy.