Is it possible to remove wheel without loosening the (V) brakes I have a mountain bike with V-brakes and every time I get a puncture and need to remove the wheel to replace the inner tube, I have to use a hex/Allen key to loosen the brakes, otherwise I can't pull the wheel out.

Is there a way to loosen the brake arms without fiddling with the hex/Allen screw? I'm worried about wearing the screw out.

Just to clarify, quick release isn't good anyway, noodle still won't come out and I still have to loosen the cable.

Adding a photo of noodle in question, as suggested (I've moved the cover to the right to fully expose the end of the noodle):



Another photo of noodle with breaks released:



And one with breaks engaged (apologies for the blurriness, was a little tricky holding my phone and engaging the break):



And finally, one with the arms pinched:
Yeah. Use the quick release. 



If you push the brake arms together, you should be able to pull the noodle out of the noodle holder (you may need to wiggle it a bit out). Then the arms will be wide enough to remove the wheel.

Alternatively, you can de-inflate the tire, remove it and then re-inflate it after re-installation.