I weight about 40 lbs (18 kg) more than the weight limit for the trike I can afford
Answer: Maybe - speed isn't the problem.

While most "limits" have generous tolerances, your manufacturer's warranty could be unusable if there was a structural problem.

Your brakes would have to dispel more momentum while stopping, so that will increase wear and runout distances.

Riding is a great way to get exercise, and I've successfully ridden road bikes while being at the upper boundary of weight.  



Suggestion: can you try a spin bike at a gym?  Could give you the cycling motion without needing to be on a bike at all.  They are heavy, solid and stable so you're not going to fall off.