I do not think it would be practical at all to walk to Grand Case for dinner, as it is a long walk and probably after dark, which would NOT be advisable, from a safety standpoint. Restaurants in Grand Case could call you a taxi yes, but it could take a while for them to come. There are plenty of taxi vans in SXM, yes. Public transportation in SXM is NOT dependable at all, in terms of running on a schedule, etc., and would not be at ALL convenient to where you are staying. You would have to walk a LONG way to where you would pick up the bus, and you may wait an hour or more for them to come.
For a cab, if you decide to go that way, suggest you contact TTOL sponsor Wilfred Brooks. He has a large van, is a very safe driver and a heck of a nice guy. You could probably work out some type of a deal for him to be on call for you. You would need to get a phone to contact him, but you should do that anyway.
I have to ask, though, why is it that you are not planning on renting a car?? If it is to save money, I guarantee that you will spend more money in cabs than a rental car will cost. If you are worried about driving on island, it really is pretty easy, and they do drive on the 'correct' side of the road. If you are worried about drinking and driving, how many adults will you have? If you have at least 4 adults, designate one person as the designated driver each night and switch off.