Fallout 4 on vita without a ps4
Solution 1:
You can't.
The only way to play Fallout 4 on the Vita is through the PS4's Remote Play feature. If you no longer have access to a PS4, you're missing the core infrastructure required to make this work. No PS4 = No Fallout 4.
Solution 2:
Remote control is not the same as independent play on Vita. Many people wish at least PS2 games on Vita or GTA4 but Fallout... Vita is too weak for F4, even for F3 and moreover for market and developers this console is "nearly dead". So you should come for new PS4.