Catherine Jo Morgan wrote...
Could a laser level lay a straight
line onto the curved surface, so I could mark it for cutting?

Yes, the "Strait-line" style lasers will work for something like this.

Are the lines or dots always smaller the closer you are?

Yes. Although much narrower than that other light sources, the beams of
these cheap lasers do diverge noticeably. The ones with a finer aperture
have thinner beams. If you can modify one to have a very fine aperture
(I.e, very narrow slit in very thin material), it should be able to do
what you want, within reason. You'll still get a diffraction pattern, but
the main line should be pretty clear for reasonable distance.

Also - would it be kind to my eyes to wear shaded glasses when using a laser
level?

Doesn't matter. The lasers in those things are too weak to pose any
serious hazard. It's about as dangerous as looking at something
illuminated by a red flashlight.

Cheers!

Jim