There are two ways to catch him without chasing him around, which won't work anyway.
The first is to make a long pole with a T on top of it, just long enough for him to perch. Wait until a dark night, and slip it up under his belly and watch for him to step up on it. Then lower him down gently. On a moonlit night, don't be surprised if he pitches out of the tree and flies away.
The second way to catch any game rooster, that works exceedingly well, is to use their territorial instincts to you advantage. Another rooster placed in a cage in on his turf will make him throw caution to the wind. As he postures with his hackles fanned out, it is a simple matter to walk up behind him and pick him up. This method is still in use to catch red jungle fowl by primitive hunters. Undoubtedly, this technique played some factor in the early domestication of the chicken. With today's modern technology, it would be quite possible to use this technique to capture him. A smartphone with a crowing rooster downloaded and set as an alarm tone, with an alarm set to sound every 30 seconds should lure him right in a coop, rig a rope to pull the door if you have to.
Once you get him caught, you can put him in a small pen and tame him. Once he looks to you for food, you can start handling him and he should tame right down, but he may still want to roost in a tree, where he doesn't feel cornered. You could just get the vet to dub him, (or do it yourself) and then let him be a wild thing with no fear of frostbite. They can do quite well, and I wouldn't be a bit surprised if he made you a pretty good weather indicator. If he is like any that I have had, he will be high in his tree most times, and if it is going to be really cold, he will be in with the hens, or at least lower and out of the wind.
I wouldn't worry about his spurs until they get really long. The games are usually pretty light on their feet and don't damage the hens as bad as some of the heavier clumsy breeds.
The main drawback is, that when you raise birds from him, he will not tolerate his sons once they reach 5 to 8 months of age, and his daughters may want to roost in the trees instead of the coop. If you wish to eat the excess cockerels, the crosses are quite tasty and with ample breast meat, yet a little firmer than most chicken, more reminiscent of a wild game bird, like grouse or pheasant.