MadCrazyHunter, your from Texas right??
In Texas you can trap/transport/relocate hogs any day of the week if you want to. They are considered exotics and/or pests, so there are very few rules/regulations concerning wild hogs.
Javelina are a different story. In Texas they are considered a game animal, so you have to get permits and all the BS that goes with it. Personally I have never heard of anybody trapping and relocating javelina, so I dont know what kinda of tags you would need. Of course you dont have to get the proper tags to trap and relocate a javelina, if a gamewarden catches you, you could always the dumb kid role.
To be honest there is not much point in trapping just one javelina and moving it.
On the ranches that I manage, we trap and relocate deer on occasion. We have to get TTT permits each time we do it. There are alot of BS that goes with it and some times it seems like its more trouble then its worth. So most of the time I let the ranch secretary take care of it.
To be honest there is no point in trapping and relocting just 1 javelina. Where you catch 1 javelina at, you can reset assure that there are probably dozens more running around. It would be alot easier to just shoot each one that you see. Just because you dont eat them, dosent mean that you shouldnt try to control there numbers.