Will the 8163x optical power sensor modules operate with both SM and MM fiber?

Yes, you can use the Keysight Technologies optical power sensors with both single mode (SM) and multimode (MM) fiber.

The 81632x and 81635x modules have straight fiber on their input and power on fibers with a core size of 62.5 micron (NA < 0.24) can be measured.
The 81633x and 81634x modules have a recessed lens on the input. The light goes through free air, to the focussing lens, then via fiber to the detector. Fibers with a core size of 100 micron (NA < 0.3) can be measured.