Where can I buy parts

I'm not aware of a source for Conair hair dryer parts; definitely doesn't appear you can get them from Conair.

Which leaves us with the fact that manufacturers most often will buy off the shelf parts like switches rather than take the time and engineering to design custom switches. I found a video showing a teardown of the dryer and it doesn't look to me like those are anything special. Places like mouser.com or digikey.com carry hundreds of different kinds of switches, so it's very likely you can find a suitable replacement online.

However, the thing is you will have to open up the dryer and measure the switches plus determine how many wires go to it and how many positions it has. Once you know all that it's then a matter of searching through those hundreds of choices to find one that's compatible.

Occasionally there will be markings on the switch that could help, but that's not something you can count on.

My suggestion would be to watch this video and open up the handle to access the switches, if you haven't already.

Conair 1875 Hair Dryer repair and troubleshooting - YouTube

Next, get some calipers and measure the dimensions of the switch; length, width and height. I'd suggest using metric dimensions (centimeters) if possible, as parts are being made to those specifications more and more as opposed to US standard (inch) measurements.

Finally, take some high resolution pictures of the front, back, sides, top and bottom of the switch and add them to your question.

Adding images to an existing question - iFixit Repair Guide

Armed with that data, those of us with experience in searching the parts lists can see if we can assist you in finding a replacement that'll fit and work.