No, you cannot use a Zapper with mame, there is no way to interface it with a PC. There are no light guns from any console that will work directly, with the possible exception of a Guncon 2 which I believe was for sold the PS2 but this uses homebrew drivers and may only work on windows XP.
Early on I experimented with a Wiimote interfaced to a PC, it worked but was troublesome and constantly lost sync, so I cannot recommend that to you.
But, there are many other options you can use, for example the Ultimarc Aimtrak
https://www.ultimarc.com/aimtrak.html this is what I will be using on my multi cabinet, there is also the Arcade gun
http://www.arcadeguns.com/ which I believe is just a prepackaged Aimtrak setup there is also the USB2Gun interface, which allows you to install real arcade guns on a mame cab.
there is the Act Labs gun
http://www.act-labs.com/, keep in mind the Act Labs guns and and the guncon need a CRT monitor to operate, while the other options (should) work on any type of display.
Light gun interfaces are not cheap, so you won't be able to get a good set up going without some investment.