Well, you have not told us your level of electronics knowledge, skill, equipment, etc. But, assuming that you have the basics...
You might possibly find a part number, somewhere on the switch... On the sides... Maybe, even the bottom... A part can, often, be identified, from a google search, of the number.
The switch is surrounded by through-hole parts. It might be easier to remove those, to get a look at the sides, than removing the switch.
If you don't find a number on the sides, you may have to remove the switch. This will require some desoldering skills. You can get those from YouTube. You need to have good skills and equipment, to desolder, as it is very easy to tear off a soldering pad.
Search for a service manual ( not the operators manual) for the device. Call the company, ask to speak with a repair tech (not customer service, though they may be helpful, too.) I have had companies send me repair parts, for free.
If you are in a go-for-broke situation, there would be no loss in starting by removing the switch. If you are ready to do that, take pictures of the pin-side of the switch and post them. We'll try to give you pointers.
Look on Ebay, for someone parting out the same device.