"Do the ones in your link fit a regular 3 jaw drill chuck?"
Nope, sorry; those and the majority of annular cutters use the (for mag drills, anyway) "standard" Weldon chuck, 3/4" diameter with two flats/set screws - it's a more rigid mount, and deep annular cutters do NOT like side-loading - they tend to shatter with too much wobble. This
G&J Hall Tools 18Y17 Powerbor Weldon Chuck Adaptor, 1/2"-2 UN Thread Fitting, 3/4" Arbor, For All Electromagnetic Drilling Systems: Drill Press Accessories: Amazon.com: Home Improvement
is what the cutter shanks look like, the female of that is the norm for most mag drills.
Your loaner drill sounds like it has the (normally extra cost) 3-jaw chuck on it, might wanna ask if the Weldon mount is available for it if you're interested - maybe if the owner has that he'd be interested in gaining a cutter for the use of it. If there's TOO much "monkey-motion" involved tho, it might not be worth it to either of you
Sorry if I seem to be pushing spendy stuff, I just got hooked after trying too long to drill too big holes with hand drills - so far, my mag drill has its own "drilling station" I built, capable of drilling a 1-1/2" hole in a 2" square block of steel if I needed to. It'll also drill evenly spaced holes (has its own x-y table) over 12" distance per setup, drill exactly centered holes in square tube up to 3", and probably a dozen other things I've yet to dream up for it (including eventually building a line bore setup to re-bush parts of my backhoe) - at this time I've picked up cutters from 1/2" up to 1-1/2", including a few metrics; all in 2" depth of cut.
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Did I mention I'm addicted??!? :laughing:...Steve