Question about Bris/Conversion

My son was adopted from Guatemala and came home at the age of 4.5 months in December of last year. We were told by our pediatrician that he could not have a circumcision until he was 1 year old and could withstand the anesthesia. He is now one year old, has had his physical and went to the pediatric urologist. He has another medical issue which is being addressed by surgery and at that time, he will also be circumsized. There will be Rabbi present to preform the bris. It is my understanding that he will then need a Hatafat Dam Brit which is the ceremony in which he will receive a pin prick rather than be circumsized. My question is what comes first, the conversion (mikvah) or the Hatafat Dam Brit? I have received so many different answers and would love to know about your experience. We were hoping to have a the Hatafat Dam Brit at the house with family then do a formal baby naming at the synogogue to include our Temple "Family". But, where does the Conversion fit in? Any advice would be greatly appreciated. Thanks!