Important to use a small frame or mini pump properly, especially for Presta.
One has to support the pump/pump head and wheel when pumping...
1. When putting the pump onto the valve - put thumb on tire, directly above where the valve is located - that will allow the head to be pushed on without damage to the valve/tube.
2. Support the pump (as shown in pic) with the thumb curled over the top of Tire/wheel. Support the pump head side with the index/fore finger, support the pump head below/around the barrel of the pump. No real need to use the ring finger or pinky - but you can if you want to.
3. Don't 'lean' the wheel against anything, allow it to move as your pump hand might move - pumphead / valve at top most position.
How to Properly handle/cradle a mini pump
4. When done, to release the pump off valve - DON'T try to wiggle the pump head off. Unlock any locking lever, pump and valve still at topmost position, wheel on solid ground. Hold the pump barrel (mid or pump handle area) with one hand. The a quick downward rap of the free hand, onto the barrel directly near the pump head. It will disengage without any valve damage.
Done.
This was especially important when working with delicate silk or racing cotton tubulars which often had very light Latex tubes sewn in... But works for any direct attach pump.
You could get a pump with hose and screw-on head - but those often lose pressure as you unscrew the head... your choice.
Ride On
Yuri