Can I get the Ray Gun Mark 2 if I have purchased Vengeance Map Pack but not the DLC Season Pass? I do not want to have to buy the Season Pass, and I hope that I can get the Ray Gun Mark 2 without it.
Yes, you can.
From the wiki
The Ray Gun Mark II is a wonder weapon that was released alongside the Zombies map, Buried, and is featured in all Zombies maps in Call of Duty: Black Ops II (only if the player has downloaded the Vengeance map pack).
Basically, the reason people with the Season Pass get this weapon, is because they have effectively pre-purchased the Vengeance map pack, but anyone who purchases the map pack separately gets it as well, regardless of what they do/don't already have in terms of other map packs.