Reporting question for Switch Tip - Fender®, Telecaster "Top Hat", Black

Product:
Switch Tip - Fender®, Telecaster "Top Hat", Black

Question:
Your spec's on this don't say what shaft size it fits. This pickup selector is part of a four way switch so not OEM. The knob that came with it split in two (the whole knob). The replacement Tele knob I got for it is too small for the shaft. The shaft measures 0.197 in. Will your know work here?