For anyone who will not have the space to have both the .vpk and installed payload (i.e. you have a 4gb memory card), this is what you do.

(Thanks to this comment for inspiration).

On your PC, open up the .vpk with a program like WinRAR. In there, extract out only the eboot.bin + sce_sys folder. Place those two files into a .zip, then rename that .zip to a .vpk file.

Transfer that file via FTP to your Vita. Then, install that .vpk file to your PSVita with VitaShell.

Afterwards, copy over the rest of the game contents with FileZilla into the folder that the vpk installation created.

And no, you cannot copy all of the game's contents (including eboot) at once, because when you install those files with VitaShell, you are making it remake the eboot.bin and sce_sys folders so that the game will work with your specific system.

Hope this helps all of you (like me) with small cards! Don't forget that you need to be in Henkaku mood to enable booting these games.

EDIT:Clarity.