The oils in the strop could become thinner giving you a better stropping effect but malleability of the steel can't be affected at that temperature... as far as I know.
Expansion & contraction is a scientific fact & steel will expand 0.12% at 180ºF. I don't know what consequence that would be to stropping.
A change in malleability tho seems to imply a change in temper & hot water simply won't do that to steel under Newtonian physics.

Maybe Quantum physics at work & you may be 100% right about the malleability but the Heisenberg principle says I can't be certain.