So I see a lot of Mods on the Nexus that are Tattoos for Females (Usually Type 3), and all the mods seem to specify using a female character. But here's the thing: I really don't play Female Characters very often, so I was wondering if there are any Tattoo packs floating out there for Male Characters? Can the Tattoo Packs available be used with Male Bodies?

The first one that comes to mind is for FO3 but it should still work fine for NV, as I've copied other body textures over, both male and female. It's " Mavroshs Alternate Textures For Breezes Male Body Replacer ." Not sure of any for vanilla bodies, though.
I don't know of any listed on the NV Nexus side.

So just throw them in my New Vegas Data Folder?

If you use FOMM it's better to create a fomod if you want to uninstall later makes it a bit easier, and less cahnce of something being left behind.
But, open the folders and if the structure is like this - textures\characters\male - then just drop it in. I'm sure most of the files all still go in the same places.

Edit: Earlier while browsing I just typed Breeze into the FO3 Nexus search box and there were some other tattoos as well. Assuming you use Breeze's.