I usually tie a line around the mast to whichever device I am using to climb the mast (bosun chair, climbing harness, ATN Climber). Tie to one side of the climbing unit, pass around the mast, and then tie to the opposite side of the climbing unit. As there are no stays on a Nonsuch mast, there isn't anything to grab on to to prevent you from swing away from the mast. This line will help keep you in place, so you won't need to wrap your legs around the mast to steady yourself (gets tiring if you are up there for any length of time).
My boat has two halyards. I do wrap the 2nd halyard around my torso and have someone take up the slack on the winch, as a precaution against the something on the primary gear failing.
Also make sure all of your tools are secured to you (or at least that the bag you use to carry them up is secured to you and is deep enough to keep the tools in it)... a wrench, socket, pliers etc can make a nasty crack or hole in the deck when falling from about 50ft (15mt), or makes an upsetting splash if it hits the water and sinks to the bottom (if you are doing this when not on the hard).