As an ex-hiking/mountain bike guide in Tobago I can easily say Castara is a great place to be based for outdoor adventures and laying around.
And because of the steep terrain in that part of the island high-heart rates can easily attained.
Guides who focus on the fitness side of rainforest activities are next to impossible to find in my experience. The Bird-Watching Guides mytobago's page have listed are birders first and foremost but if you were to contact any of them and explain to them your request they may be able to help.
In my opinion it's pretty safe to hike around the rainforest. There are no poisonous snakes or spiders. The biggest dangers would be uneven terrain, thorny trees/shrubs and getting lost. Since many trails in Tobago are hardly used anymore some are very grown over and some simply aren't there any more due to trees falling and a very heavy rainy season. Let someone you trust know where you're going, just in case you get lost. Unlike the UK where dense heather/pine/foliage might hamper or slow a hike, dense jungle stops it, so don't try to go any further if you see a trail deep into the jungle get bushy cus it'll probably get even worse!
For our tours we used to park at the top of a place called King Peter's Bay and walk to the beach the walk/run/ride back up. Sounds easy but you start at around 1200ft (400m) descend to sea level via a paved road turning into a jeep road, relax on the beach or if you know what you were doing, go to the two super special hidden gem beaches north or south of that then return the same way back up!
You also could to try Gilpin Rainforest Trail on your own but I wouldn't park my car by the start where guides hangout. Park your car by the lookout, then walk to the trail head, do the entire trail making sure to take a left where the trail comes to an obvious junction after more than an hour's hike. This takes you back to the road, and you gotta walk back up on the paved road back to your car but the road more or less quiet and hardly used.
There used to be a trail in Castara that could take you across the Rainforest to the capital Scarborough but that trail has become nearly impassable last time we tried a few years ago. There's a great trail to a beach called Nigel's Bay or Major Bay after Castara and before Little Englishman's Bay but I forgot how to get there, either a mytobago-er can help or a Castara local for advice. Also if you're headin north after Castara there's a sign-posted jeep road on your right called Sawpit Trace that we followed before and despite getting lost on a few times has some great views if you care to walk on it for a bit.
If you want some more trail ideas I'd be happy to help.
Can't wait to get back home myself and GPS these trails! Hope y'all enjoy y'all stay!