Yes. Stay at a place that supplies kayaks and is near both the reef and some bouys (generally north - the reef is a quite far from shore in the southern resort areas)
Los Encantos, Caye Villas, El Pescador Lodge/Villas, Belizean Shores and/or Journey's End could all fit the bill. Maybe Captain Morgan's supplies kayaks too - check with them.

Serious Advice - don't even think about "surfing" the reef and pumping your adrenaline by going into the deep water "outside" - every season somebody tries it in a kayak - ending up loosing gear, kayak, blood and damaging precious coral. That is a GOOD day outside the reef in a Kayak - a bad one can be fatal.

Do not do this on a day when there is a "northerner" blowing - that is when the wind blows "from the back" and will take you out to sea ...... next stop Turneffe or Jamaica. Not good.

Places up by Mexico Rocks would be excellent locations too - I don't know who supplies kayaks in that area.

Be sure you are a good swimmer, have a snorkel-buddy along and are generally capable/comfortable in the water - I have rescued one too many individual who tipped over, lost paddles and freaked out - no need to have such an upsetting event mar your stay.

Enjoy!