Both destinations are served by Jaipur (JAI). Since there's no flight route between them, the best way to travel is by road.
Khatu Shyam
Fly to Jaipur (JAI), then travel by road to Khatu Shyam. Taxis, buses, and private cabs are available from the airport.
Pushkar
Fly to Jaipur (JAI), then travel by road to Pushkar. Local transport options include taxis, auto-rickshaws, and state buses.