Pulling it off without soldering will be tricky, your only option will probably be to get a chunk of coax with the connectors already on it, cut off a connector, then use bolts and crimp on lugs to connect the coax to the antenna element.
You're finding multiple descriptions of how to do it because there are multiple ways of doing it depending on the intended use of the antenna.
You can feed it directly like a dipole, splitting the driven element in two and connecting one side to the coax shield and one to the center conductor of the coax. It will not be possible to get maximum bandwidth and maximum gain with this method, though you should be able to get a reasonable compromise that works on all of 2 meters. 70cm would be much trickier.
You can feed it with a gamma match. This gives a wide match and has the advantage of also acting as a balun. They're finicky to make, and would be very difficult to tune without an SWR meter or antenna analyzer
You can feed it with a hairpin match. Similar problems to the gamma match, but similar advantages.
Personally, I'd recommend finding a design that specifically calls for a directly driven element. Google for NT1K Tape Measure Yagi for a good project write-up.
Another option if you don't need portability would be to ditch the yagi and build a cubical quad instead. There are many calculators available online that give you all the required dimensions, and they tend to be a bit more forgiving on the SWR front. They also provide more gain per element than a yagi, at least until you get out to about 7 elements. They can be made very inexpensively out of PVC or wooden dowel and 1"x1" hardwood lumber for the boom and wooden dowels for the spreaders.