NO barbeque shrimp are not usually sautéed in butter, they are tossed in melted butter, aromatics and spices and spread in a shallow pan and put in the oven to 'bake'. One can certainly sauté. The finish is slightly different. In a moderate oven with plenty of butter -- a requirement -- the shrimp both poach and roast in the butter. They are served with plenty of bread for dipping. The shrimp used are most often head-on; this allows for sucking the fat out of the head when the diner pulls it off. (An unpleasant image for some, but this is standard. It isn't required, of course, if head-on shrimp are not available.
Compound butter is whole butter mixed with flavorings -- spices, wine, juice(s), aromatics; any, some or all -- formed into a log, rolled and chilled. There is no need to do this for something like barbecue shrimp because it is necessary to melt the butter first. One can easily and simply combine the melted butter with the seasonings and aromatics right at the time of cooking.
Compound butter is essentially a sauce that is kept cold, and thus firm, so that it can be cut and placed on a hot item (steaks or fish right off the grill, e.g.) where it then melts at a moderate rate and is still melting (one hopes) at the time of service.
Compound butters are easily made. I often make 4-6 types at once, using, say, 5-8 pounds of butter. One allows the butter (use unsalted) to just soften, then, in my case, I divide the butter into 5-8 bowls, mix in my prepped ingredients into each, then stick the bowls in the fridge to firm a little. After this happens I remove the butters one at a time, fashioning a 2-inch log out of each butter on parchment paper, rolling the paper around the log and twisting the ends. These then get wrapped in plasic and frozen or fridge. Voilà -- instant sauce at the ready for steaks, grilled or roasted salmon, whatever.
Btw, for the best compound butter using Worcestershire, use Worcestershire powder instead of liquid. Better mixing and better flavor.