Well, going to BubbleMan last would mean that it would take 7 metal hits instead of 28 (and I'm quite sure that they would take less time per shot since you can aim the metal weapon), which, according to the comparison of the fight with BubbleMan on Morimoto and Finalfighter's run and the fight on Morimoto's old version, saves about 10 more seconds, from about 13.41 to 3.55 (using a stopwatch, from the moment the bar is filled until the final hit).
For the HeatMan fight, there seems to be about a second of delay in between each hit, and it would take 14 hits compared to 5 with bubble lead. (info taken from
http://www.mmhp.net/GameHints/MM2-Data.html#Damage ) That would take up about 9 seconds, assuming that the fight would be pretty much the same with bubble lead compared to the normal weapon other than the number of hits.
There would be one more weapon change once in the boss room for BubbleMan, but it seems that the bubble lead weapon travels slower than the regular weapon, saving some time ideally. But all of that is small in comparison to the large difference we're hypothetically getting.
But I haven't personally done a fight with HeatMan using the normal weapon, so there's likely some issue there.