Depending on the era, it may refuse to work with something that doesn't ID itself as a compatible charger. Otherwise, a "laptop charger" is really nothing more than what you describe: a 12/19V (as appropriate) power supply. The actual battery charging is handled by the circuitry in the laptop.
An off-brand Thinkpad compatible charger shouldn't be that expensive. I don't think you'll find a suitable generic power brick much cheaper, and a proper "charger" would be plug-and-play. They have to put out a decent amount of power. 60W is about the minimum you'll get away with, and most will want more than that should they decide/need to charge the battery. This is a lot more power than your typical "wall wart" puts out.