So, first I'm just making sure. No screw or dial face... just plain missing and a gaping hole?
If you set it to 220 and leave it there, it will set the little claw that runs along the counter wheel. Two groove are cut on the wheel and normally the 10 part would cause the claw to push out and stop the shutter from being engaged. The 20 groove is just longer and no other tension devices are set in the winding mechanism, but you should set the film pressure plate for 120 or 220 depending because the tension needed to keep the counting roller is different from the winding mechanism and as you, paper backed and no paper backed. When you come to the end of the 10th shot and you'll have to shoot two more to wind past the edge of the film. Also, you'll need to fire off the shutter when the back is open to reset the counter because the counter is still looking to go to 20 and you opened the back while the system was still engaged and cocked to go.
Have you contacted Pentax parts to see if you can still order the selector and screw?
It should be...
1 CNL-D1.4x2.2
1 C105 - Frame Nut Control Dial
...assuming that you still have the rest of the parts still there including the plastic dust shield around it all.
View of the counting wheel and the claw that rides the groove... a crappy picture, sorry.
The tip of the claw in this image show that it is riding up on the groove as if the 10th shot was down and only winding on is allowed.