Always degauss first. Any time you do a tube swap, you should degauss the tube before even thinking about trying to converge it. You'll just drive yourself nuts.
Now, what you aren't clear on, was if you swapped just the tube, or if you swapped the tube and the yoke together. If you didn't remove or swap the yoke, you shouldn't have to adjust it, since it was already converged when it was in the television.
You don't have to buy a degaussing coil. You can make one easily - simply take the degaussing coil out of a junked 25" or bigger TV set, coil it up, and put a power cord on it. Just don't leave it plugged in too long, or it will melt.
-Ian