I briefly considered a 2p run as that would give some more room for target shooting and most likely would save time in some parts.
The main reason i abandoned the idea was because the game doesn't give you twice as many upgrades. That will be a problem with the speed upgrades. The first speed upgrade in area 2 is very early on, while the next is only much later (links to area maps:
https://kb.speeddemosarchive.com/Ikari_Warriors/Level_Maps). Part of the distance could be dealt with by killing off player 2 at regular intervals, but you don't have enough lives to cover the whole distance this way, which meant using the continue code (ABBA). The continue code is a cheat code so I didn't feel that was the right way to go.
There were a couple of other concerns/questions as well that I had about how a 2p run would work out, but I didn't see a way forward with the speed thing so I didn't spend time on investigating them.