You can also use a wine cork for the stopper. Might be cheaper and easier to find. You can easily shave the end to fit into the valve.
Another trick I learned for using an inflator... each time after pressing the air out of the inflator into the mat, quickly spread the wide opening of the inflator and give a short puff from your mouth into the inflator, then quickly rolling the opening closed. It works much better than trying to scoop air directly. This way you don't need much space in the shelter to get the inflator filled with air.