Adding push button to CC DC to DC converter to adjust CC
Yes, it would, but probably not too severe -- and "too severe" depends on your situation, so you'd need to test.  

You could make it a bit better by putting a low-value resistor in series with the button.

You could make it better yet by using a momentary-contact, break-before-make SPDT switch that disconnects the load and then shorts the terminal.  I'd still use the above-mentioned resistor, though.

To actually find the switch you'll need to go shopping -- they're out there, I can't recommend a part number, and it just feels like this is the sort of thing that'll be more readily available as a toggle switch than a button, but that's for you to discover.