I have a Küng tenor (rosewood, single-key). Wonderful warm tone. FAR FAR better than anything Hohner ever made. Very unlikely to be varnished, so an oil finish sounds right. Küng make recorders at several price points and change their designs frequently, so you need a lot more information than just the brand name to work out what it's worth.

Mine was clean when I got it (second-hand, 15 years ago) and I haven't needed to whack the block out yet.

I have one very old recorder (made of cocobolo) where the player's mouth has leached the wood a bit. I treated that area with vaseline - cocobolo is violently irritant, allergenic and toxic, and I didn't want any liberated wood toxins getting into my lips. All rosewoods are toxic and allergenic to some degree, so if there's any chance this instrument is made of one, I'd use something that provided a better barrier than almond oil.