Incorrect. Lead paint was still being used in commercial applications into the early 2000s. So yes, 90s pins still had lead paint.
Normally, it's not dangerous unless you're sanding the paint and end up inhaling the dust. In the unlikely event that you need to sand the paint, you should use a mask and eye protection.
Quoted from Isochronic_Frost:
Solder is partially lead but you should be fine. Just don't be melting solder and breathing the black smoke directly.
Lead is not really absorbed through the skin, but it can be transferred from your hands to your face, eyes, nose, or mouth. I generally use gloves when handling solder just as a precaution (and for a little bit of protection against splashes of hot solder and flux).
The fumes from the rosin in solder are toxic. Only solder in a well ventilated area and/or with a fume extractor.
Quoted from Islote:
But is there any other kind of hazardous substance I should take care of like asbestos or something?
There is no asbestos.
Parts are made of steel, aluminum, zinc, nickel, and brass. Brass is seldom used, and is typically just for the tilt bob ring and some screws. Anything that is plated is usually nickel, unless it's an aftermarket mod (and in that case, sometimes it's chrome or brass). Sometimes the tilt bob is graphite. As long as you don't try to lick anything, you should be fine.
If you are putting metal parts in a tumbler, you should use a mask and gloves. There will be a lot of very fine metal powder produced as a result of polishing parts in a tumbler.