I'm thinking the same as Howie: nothing is impossible, but it's probably not worth it.
You are right about the transponder chip in the key---you could probably just skip that part of it.
If you were to take apart a donor Jetta, you'd find that it has a traditional ignition switch just like any other car, with heavy-gauge on/off wires coming out of it.
Then, separately around the keyhole, is a "ring" that's a receiver for the transponder. You could eliminate that part (either throw it away, or leave it in there but unplugged, whichever looks better), and then put the regular ignition switch in and use it.
The keyless would be the harder part.
Most modern cars no longer have a separate keyless entry; it's part of the car's computer system.
For example, my 1996 Buick Roadmaster wagon has a dedicated keyless entry unit behind the panels in the cargo area. I could theoretically remove it from the car, get a GM wiring schematic, figure it all out, and install it in another car and use my GM remotes.
But the newer cars are different. Just for an example, the 2003-2007 Accord actually uses the driver's-door power window switch as its keyless receiver, and then sends lock/unlock/trunk/panic info into the car's main body computer (which is part of the fuse box) by data........
I suppose it would be possible to take the Honda fuse box, Honda window switch, all associated wiring, and try to stuff all that somewhere into another car.... but it'd probably be a week-long project, with no guarantee of success.
If you're really serious, your fist step would be do thoroughly examine the electrical diagram for the donor car you're considering, and then go from there. Either find a friend at VW dealer, or pay a few bucks at www.alldatadiy.com
I'm not sure if you're set on all-VW parts for your Beetle, but a favorite of car-customizers are the 1980s-era GM tilt steering columns. You'd have your turn signals, wipers, and maybe cruise control right on the turn-signal stalk, tilt steering if you want it, telescoping steering wheel (if you get it from a Cadillac), and a semi-modern ignition lock with probably more security than the original Beetle dash switch.
You could get one of those columns from a junkyard, but there are also companies that make them in billet aluminum or maybe stainless steel too.
If you just want something that's a little different, maybe you could find an aftermarket system with plain-looking remotes and then pay someone to silk-screen the VW logo on them, or have some small stickers made.
By the way, again if you really have unlimited time and/or money, I remember someone telling me about a kit car made to use the entire drivetrain from a Subaru Forester. That is, you'd put the kit car together, then find a totalled Forester and transfer the engine, transmission, suspension, 4x4 stuff, and wiring and computer over into the kit car.....I'm not sure if the OEM Subaru keyless would still do anything, but it's a possibility. Maybe someone makes some similar setup for Beetles, who knows?