Following is my reply to the same question 4 months ago on a sailing forum.

Picking up a mooring alone need not be an issue. There are probably as many ways to do it as there are people sailing. My employment causes me to move a variety of cats and monos from 36'-50' alone and I've come up with a method that has served me well for many years. Rather than the "standard" way of slowly motoring directly into the wind, I aim for a spot 6'-10' upwind of the mooring with the boat on a 45 degree diagonal to the wind. With the bow(s) a few feet past the mooring and a shot of reverse to completely stop forward motion, one can casually walk forward with the boat hook as the boat is slowly drifting down to the mooring. I just did this Monday at West End Tortola with winds 25 gusting to 30kts on a 44' cat without issue. For me it's much more difficult to stop a boat dead into the wind with the nose right on the mooring and not have the boat blow away before the painter has been retrieved and connected via a line to a cleat. Since I'm jumping from boat to boat I rarely get a chance to spend a lot of time really getting used to the manners of all the boats in all situations. Letting the wind push me to the mooring while I am patiently waiting with the boat hook makes it nearly foolproof.