How do I play special ops without upgrading my weapon?

You cant. You need a weapon powerful enough to progress.

You can but you will struggle. I currently have to use a Vektor pistol in special ops as that weapon is the only one with enough stopping power to be competitive. I am beyond the last level and just building bank account and gems till next level and guns are ready. Currently $130 billion and 5000 gems. Newcomers to the game would be jealous but the truth is that the money is useless once you have nothing to spend it on in the game.