how both of them get in touch with you? recommend by friend or ?
If you are hesitate to passed the key to agent, and uncomfortable for exclusive sell, then you can take the photo very very nicely and find those agent at property search engine show area specialist, and ask them to sell your unit openly without exclusive.

It depend on you are rushing to sell or not, and do you can fully corporate with the agent anytime* they bring prospect come to house visit, and you can fully corporate with the agent attending the home visiting process.

or i can suggest you install moveable / non permanant cctv (with wifi on) for your surveillance. then you will less worry about your house condition even passed the key to agent.