I used an agency at both ends because I was terrified of something going wrong and the cats ending up at the municipality! But if you look at Dubai Kennels & Cattery (DKC) website they have an very clear section which sets out what you need to do, if you decide to do it yourself. Good luck!
Not sure if this is the same place but I just visited Kyra in the Gold & Diamond Park and they were excellent. I had to have my new tragus and helix piercings removed for an MRI and they did that and put them back in afterwards for me. They were really gentle and careful and I couldn't recommend them highly enough. Note I didn't get the original piercings done there, I had them done at a pop up place in Dubai but regardless they were super helpful. I'd definitely get any further piercings done there and they were very popular so it seems other people feel the same way. Can't advise on the headache thing though, sorry about that.