I'd suggest looking at a paddle-foot pistol. The range is better and you don't need to reload immediately after firing.
As a primarily missile weapon using character precise shot is required, which means point blank shot is required.
Explosive missile requires L4.
Chemical stability (gun chemist specific discovery) has no minimum level and it'd be better having it take up a low level slot than a high level one, and you will want it eventually.
Unless and until you get exploding bullet (another min L4 discovery) anything which requires a splash effect doesn't work. And exploding bullet is marked with a star which means it won't work with most such, including smoke bomb. Can that idea.
Like I said, at the start
1: point blank shot
Gun chemist 1: gunsmithing
Discovery 2: chemical stability
3: precise shot
If you're going to ~11 then perhaps
5: rapid shot
Discovery 6: acid bomb (or some other damage type; an option that isn't fire anyway)
Gun chemist 6: rapid reload (paddle-foot pistol)
7: maybe extra discovery (spontaneous healing), or iron will, or some other defence against whatever's been the greatest danger this campaign.
Discovery 8: fast ordnance
9: weapon focus (paddle-foot pistol)
Discovery 10: cognatogen
11: overwatch style
If you don't like readied actions consider combat expertise + second chance for your last 2 feats.
Note that you can use alchemical cartridges and remember to use the cartridge savant ability from the archetype.
Egan (Ay-gahn) is a German name meaning 'fiery'. Not many English-speakers are likely to know the connotations of German names of course. You might follow it up with something in English, Egan Firehand or something like that.
