You can book with any dive company to go out to Hol Chan and Shark Ray Alley. You can dive one of them and snorkel the other. I believe their tours leave at either 9:00 a.m. or 2:00 p.m., your choice. Good half-day excursion to fit in your desire to both snorkel and dive. Then you can spend the rest of the day walking the beaches and town and eating at one of the great restaurants or bars.
Another day you can book with one of the tour companies to take you on an excursion to one of the Maya ruins on the mainland. You can either take the boat or plane over. It will be included in the price of the trip. It is an all-day trip, from 8:00 a.m. or so until 5:00 p.m. We like to combine Maya ruins and zip lining in the same day, or you can do cave tubing or Belize Zoo if you don't like to zip line. If you go to Lamani ruins you will have to do that by itself because it will take all day.
On the third day I'm sure you can find an outfit to take you fly fishing. I don't have any first-hand experience in that field, but I know some are available.
It is definitely possible to do all three if you have three full days. Then you can spend your evenings walking the beaches or the streets of the town, eating out, shopping, getting ice cream, visiting the bars with live music, etc.
Private message me if you want any specific names, places, etc.
Hope you enjoy your trip!