1- Just stain over the chink
2- Hand brush the stain on and cut in along the chink lines. Any runs will have to be addressed immediately. The stain sometimes cannot be removed if it does run onto the chink.
3- Stain over the chink and then either re-chink or tint primer to chink color and paint chink lines.
Just staining over the chink is the least expensive route. You can still see the chink, but it is subdued a little. Depends on your stain color. If you can keep up on the maintenance in bad areas you can keep ahead of the big problem of having to do the whole house.