If your tap works on your Schwinn, it will work on the Colson. Sven is right about the threads being screwed up because the steering tube is slightly out of round. If your Colson head nut fits your Schwinn, that's the problem.
When I sell a fork at a swap meet, I usually have a head-nut on it. This does two things. It shows potential buyers that the fork tube threads are good, and keeps them good. I have seen many forks screwed up because of being dropped, dinging the threaded end. One other thing, I always use a fork Jack to fix bent forks. The fork gets straightened while it's installed on the bike. There are many who comment saying ,"You don't need no Jack, just heat the bend red hot, stick a pipe in the end of it, or over it and bend it back." Be careful, that's another way the threaded end gets ruined. The threads are 1 inch- 24
Lots of old forks that have been off a bike and laying around have this problem. Carefully examine it. If its out, it can be put back in round by working it back to shape with a hammer and anvil. Sometimes all that is needed is to file the end of the threads, if they appear smashed in. I have threaded lots of forks that had damaged ends. Before you try anything, try your die again.... Are you using the proper die handle? Or did you just buy the die and have no handle? That may be your problem. Some fellows just use a big crescent wrench to hold the die. This will not work if the threads are goofed up. The die handle makes the user use both hands and keeps pressure on the die, forcing the die into the threads and giving the user control to start the die. The die handle is about 20-24 inches long. Some manufacturers heat treated the fork tubes, that's why post war to 1970's Schwinn tubes seldom bend and are harder to thread. Other companies, like Murray and Monark used mile steel flat stock to form their steering tubes and did not heat treat the finished tubing. That's why they bend so easily. Colson's , I think , were heat treated. Another good point was made by Archie, that i am not sure of, Vince could shed some light on this. On taps, there are bottoming and starting taps. I am not sure on dies. Are some dies harder to start than others?