This is what my husband is for. I’ll be on the other side of the door until it’s gone, if it’s not dead. Not sure how he feels about it, but oh well 
.
You should have sung to it @Colin, that would have done the trick 
So long, farewell
Auf Wiedersehen, goodbye
That would be a big bonus for me. I would not mind dealing with the occasional “present”
O M G !!! I am not sure how I would have coped with that. I like to see Lizards when on holiday, but couldn’t cope with one indoors, and certainly not one that size. ugh!
I’ve had a -not petsit, but homeexchange - with a serial killer cat. It wasn’t pleasant - from the perspective of an animal lover. He killed a lot of baby birds and dragged in a very much alive - and terrified - bird. As others have mentioned it must be mentioned so that you get a good match and don’t risk a sitter to pull out because you weren’t transparent. Have in place also a «rescue pack» with gloves, broom, bags, disinfectants, what is necessary.
We had great success putting a little bell on the cat. Giving the birds a fair chance, they often got away. Could be an option for the duration of the sit.
Believe it or not, he already has a bell on his collar! Not entirely sure how he caught this poor bird!
Wow, hu must be quite skillful! 
We stayed twice at the house of a killer cat with a bell and special colorful collar. The cat was quite boastful that he’d brought something through the cat door for his new bro’ (my spouse). Spouse managed to get the bird out --a little shocked but apparently not badly injured.
I mean he really isn’t which is why it’s weird! He is usually such a loaf and despite still being a kitten just eats and sleeps. We are starting to think maybe he still the bird from another cat!
I would sit for that cat in a heartbeat! Adorable. I live in a rural area and my cats are indoor/outdoor. I had a wild beast that used to bring me everything (I woke up to a live rabbit in my bed one morning). Birds are the worst–feathers everywhere! But what can we do? We love and accept them for what they are. If you lived near me I’d be happy to sit!
I am a big fan of full disclosure but I think I’d keep the live rabbit incident out of any host profile. On a sitter profile, that same tidbit probably deserves 6 
s under the Resilience category.
Anyone who grew up in the countryside would be used to it. City folk not so much. A dog I sat for caught a mouse and put it in my suitcase. So it’s not just cats.
Just be honest and upfront. You will still get lots of applicants.
“Hunting cat” is a tautology.