tips for pinching down onto an object
Here are first 3 the most simplified and generalized options you have:



All you need now is to give use more details about your needs. If you reveal more details we could help you to apply (and modify) one of these  options.

Each of above has its own pros and cons of course. You said you don't want to have spring... so maybe a rubber ;)
But in fact whole-red is one-piece-clip in which the force comes from material elesticity or stiffness.

Please tell me what is the application of such clip.