The exterior walls on my house which is made of stucco, are starting to get hairline cracks in them.
Can anyone suggest a simple, cheap solution for it that doesn't require painting the whole house exterior?
If it were my house I'd get painting! Paint is intended to seal hairline cracks of this kind. Depending on your locality you may find that it's feasible to spray a paint finish over stucco, which can be by far the easiest and cheapest way to do it.
I recently used DAP All-Purpose Stucco Patch. It comes in a tube too so you can just attach it to your caulking gun. It needs to be painted over. You need to repair those cracks so water does not get in and DAP will seal it along with a coat of paint. You'll need a plastic spreader to spread the mix.
I am fixing cracks right now for an apartment building. There is nothing I am doing that hasn't been done already. Buy some good decent caulk and run a bead over the crack then smear it into the crack with your finger. It will come back slower or faster depending on how well you ran the bead.
Good luck. Stucco is cheap junk anyway -- the lattice always rusts and expands no matter what.
Kover Krack, textured type from Sherwin Williams just brushes on the paint over.