Not wanting to be funny about this, but I think you have asked an essentially impossible question. I have no idea of what you might know or what might be considered popular where you are or in the circles you move.
Sorry.
For instance, that list of tunes you give as an example. Out of sixty I could hum eleven or twelve of those tunes (all the way through). Some others I know exist but nothing more and many others I’ve never heard of.
If you want written music I think the only answers are to look online for what you know or to go into a music shop and have a look at their books. The trouble is that I doubt many (any?) would be notated for a D whistle, which is essentially what you’d want. The tin whistle is not a “mainstream” instrument; certainly not in pop music.
In the end I suspect that you’ll simply have to learn the instrument and then play/learn most of the tunes by ear or from memory. Of the few that I know on that list, I could basically play all of them straight off. None of them are difficult tunes.
btw. as a final comment. We were once told in a session (by a rather drunk person who was becoming a nuisance) to play some “golden oldies from the '50s”. I obliged with a set of tunes … said drunken person protested that they weren’t “tunes from the '50’s”. I said that they were from the '50’s … the 1650’s.
Old/modern/popular are a matter of perspective too.
On YouTube, search for the name of the tune and you’ll most likely get quite a few examples. Note that there is no real “should” sound. Everyone plays tunes differently.
You can also go thesession.org and search for the tune. You’ll find ABC and sheet music versions. Under DOWNLOAD you can download and play a MIDI version. These are pretty simple versions of the tune which might be useful.