We are "kinda walkers" but you could run from the cut going South past Caribe Island. Of course you will have to dodge the ferry (not a problem), dodge some beach chairs at BB (not a problem), hop some sea wall borders (again not a problem), but it all can be done!
Depending on where you are staying you can run North as well, from the cut past Journey End...
We really haven't been walking North for some time but it was a good distance going North without a problem. I understand the road now goes further then JE but I would stick to the beach.
Have a great time!