Weapon groups are defined as follows (GMs may add other weapons to these groups, or add entirely new groups):
Axes: battleaxe, dwarven waraxe, greataxe, handaxe, heavy pick, light
pick, orc double axe, and throwing axe.
Blades, Heavy: bastard sword, elven curve blade, falchion, greatsword,
longsword, scimitar, scythe, and two-bladed sword.
Blades, Light: dagger, kama, kukri, rapier, sickle, starknife, and
Bows: composite longbow, composite shortbow, longbow, and shortbow.
Close: gauntlet, heavy shield, light shield, punching dagger, sap,
spiked armor, spiked gauntlet, spiked shield, and unarmed strike.
Crossbows: hand crossbow, heavy crossbow, light crossbow, heavy
repeating crossbow, and light repeating crossbow.
Double: dire flail, dwarven urgrosh, gnome hooked hammer, orc double
axe, quarterstaff, and two-bladed sword.
Flails: dire flail, flail, heavy flail, morningstar, nunchaku, spiked
chain, and whip.
Hammers: club, greatclub, heavy mace, light hammer, light mace, and
Monk: kama, nunchaku, quarterstaff, sai, shuriken, siangham, and
Natural: unarmed strike and all natural weapons, such as bite, claw,
gore, tail, and wing.
Pole Arms: glaive, guisarme, halberd, and ranseur.
Spears: javelin, lance, longspear, shortspear, spear, and trident.
Thrown: blowgun, bolas, club, dagger, dart, halfling sling staff,
javelin, light hammer, net, shortspear, shuriken, sling, spear,
starknife, throwing axe, and trident.
In this list there is no entry for the sword cane pistol, which means that the +1 bonus cannot be added.
However, if you are using the Ultimate Combat rulebook, then you will get the bonus.