The Diana 460 Mag would be my choice for a underlever hunter, hands down. It is appreciably lighter than the TX, and lighter than the HW97. It is seriously accurate out to maximum springer distances, and much easier to shoot accurately than the 350 Mag.
Unlike the TX or the 97, the 460 Mag comes with open sights and also have a stock that is conducive to using them (not a given). To a hunter, a set of opens can save a hunting trip when the scope fails, and provide a lightweight, zero cost way of shooting in their own right.
Power-wise, the 460 blows the TX's and the 97's out of the water. You might be thinking of a squirrel gun, but end up wanting to take on bigger animals down the road. The 460 Mag can be used as a true 24 fpe magnum, capable of taking down the biggest small game, or it can be detuned to any power level to suit your needs. Some guys have theirs at 14 fpe, and love 'em.
.22 cal Weihrauch barrels are notoriously over-bored, often shooting only the largest-head pellets well, likely H&N FTT 5.55. I had one of those. That's a serious downside to a hunting gun, where different types of pellets might be called for, depending on the hunting situation (inside a barn etc.).
Lead-free pellets have terrible downrange ballistics due to lack of density, even the best ones petering out at around 30 yards, so no long shots on game with 'em.
The HW's and TX's also have clumsy, metallic-loud safeties, which is a bane for the hunter. The Dianas have quieter, more functional safeties.
Breakbarrel guys sometimes point out the extra motion a fixed barrel requires, but, shooting both on a regular basis, I don't see a basis for that. With either one, you need to bring down and then back up either the barrel or a cocking arm the length and size of a barrel, which is equally bad, from a stealth point of view. Loading a breakbarrel is a little quicker / more idiot-proof than loading a fixed barrel, but the difference is really small.