The only issue I can see is that Chemist not having very many usable skills outside of their job.

If you take a look at ACN => SCH there are many skills that are still very useful or core to SCH;
Physick
Aetherflow
Energy Drain
Virus
Summon I / II
Sustain
Rouse
Raise
Eye For An Eye

Whereas your abilities for Musketeer is all DPS skills..need some utility in there.