Main reason for the nasty Zippo aftertaste that many complain about is its normally high rate of unconsumed fuel due to low combustion rate. Simply put: lot of fumes don't burn off in the flame and thus it gets passed on through the flame.
There are types of Zippos that have more efficient combustion, most notably the gas zippos that are pressured. They burn almost complete and will have no odor or aftertaste.
Another way around a typical liquid zippo lighter than can help with aftertaste (one is tasting the fluid literally) is to open the aperture of the device emitting the fuel. I would not recommend this per say, unless one does not mind dealing with the possibility of it exploding during the procedure.
In the case of the wick variants, I have always had very good success trimming the wick more and it will burn more efficiently and have less unburned vapor emitted.
David
p.s. now the axe....well that looks interesting