Stats:
gains wearer 10% resistance to fire based damage per kill, with a max resistance of 80%
50% shorter afterburn from pyros
-50% clip size
-10% resistance to melee attacks

+50% bonus fire resistance on wearer
+Afterburn gives you 25% movement speed
-Afterburn makes you marked for death
-10% slower movement speed on wearer
-30% reload speed

Maybe alt fire shoots mustard? (Jarate, anyone?)

+has a counter shot mechanic, taking damage above 50 gives your shots 15% extra damage for 1 second
+1 clip size
-25% firing speed
-10% reload speed

Since the recent change to the shortstop, and the association with fire and food:

Pros:
While active: +20% bonus healing from health packs (75 healing from medium, big fully heals)
(hidden: additional 15% on top of 20% from small health kits (36 healing from small))
At close range: ignite enemy for 3 seconds

Cons:
Passive +20% fire vulnerability
-15% percent reload speed
-20% max ammo (26 max ammo)

I figured this would pair well with the Candy Cane or the Sun-on-a-Stick. The Candy Cane since you get little over 25% of your health back from the small health drops at the cost of being easily stopped by 3 classes (soldiers, demos, and pyros). And the SoaS Since those 3 seconds if ignition would give easy crits and the fire resist while the SoaS is active could counter the fire vulnerability making the combo while the SoaS is out +10% fire resist, at very little cost other than needing to know how to play Scout well.

How about this
50% fire resistance
alt-fire sprays ketchup, slowing enemies by 30% for 2 seconds per glob of ketchup
-20% health

kinda like gas passer
+on hit drenches enemy in gas
+40% damage on flaming players
+2 clip size
-25% less damage
-10% firing speed
-no random crits

encourages hitting your shots constantly
1st shot- coats them in gas
2nd shot- ignites them (no extra damage)
3rd shot- more damage

My suggested stats for this weapon:

+Deal 200 damage gain 80% increase in fire damage resistance and full immunity to afterburn
for 30 seconds
+25% faster firing speed
+25% more accurate
-No ammo gained from dispensers whilst active