you CANNOT accurately monitor music to come out of speakers via headphones. you may well with experience find that you can roughly predict how a soundfield will be over phones, but they simply do not interface with our auditory systems the same way that speakers do.
it would be prudent to do both-perhaps the sensitivity and absurd intimacy of headphones would be best suited to get SPL matching and noise checking, but you should use speakers to see how the soundstage plays in open space, on speakers. use both, and when you're satisfied, use both again, more in a casual listening sense, to see that the overall work brings you joy (you should obviously listen to the work many many times on both, but i'm simply suggesting a method to perceptually distance the more technical work from the actual listening experience one is to derive, which may or may not (i'd go with may typically) require a little more technical tweaking for satisfaction.
what one could do, given issues with noise levels, is get a decent-sounding pair of small, sensitive speakers, and just listen at a closer distance from them than one would with larger speakers.
