Steel frames can safely be respaced, for other materials you'll have to settle for pulling the dropouts apart to get a wider wheel in. There's usually a stack of spacers(or one chunky one) on the left side of the hub. This can be replaced with a thinner one and the wheel redished if you really want a narrower wheel.
But an early 90s with a 6-speed rear? I'd have thought that they'd already been phased out from new bikes by then.

And tightening the spokes until the rim comes apart? doesn't make sense.