fogwalker, you can surely do the wire connects just as you describe, but as an electrical engineer and electronics "tinkerer" I abhor the thought! I want to know that 15 years from now my connections are still sound. twisting wires together isn't a good long term solution, and eletrical tape can come off after a few years, especially when there is a lot of surrounding heat (and humidity).
The "right" way to do it is to slip some appropriately sized heat-shrink tubing, cut to about an inch in length on each of the two wires, slide the tubing back far enough so your soldering iron won't shrink them, then solder both fan wires to the original wires on the analog board, then use a hair dryer or match to shrink the tubing. It will be a professional job that will lost as long as your classic Mac will. By the way, don't just strip off the insulation and touch both wires together and then solder them that way. Yes, the solder will stick them together, but it will be stronger and more electrically sound if you twist the wires together and then solder. Put a lot of heat on the wires and allow the solder to sink in deeply.
I know some of you lack skills and/or parts to do a job "right." But even here in outrageously expensive Japan I can pick up a cheap soldering iron for $9, solder for $3 more, and some heat-shrink for another $3. That's expensive for only one solder job, but cheap if you might be doing some electrical connects in the future.