is it safe to delete /private/tmp vs /private/var/tmp?
No.

No no no no no no no.

No.

Generally /tmp is cleared out upon reboot, but you should never just delete stuff without knowing for absolutely sure that you don't need it.

If you can't replace your hard drive with something larger and you're running that low on space, use a reputable tool that is specifically developed for the job, like Clean My Mac.