If all of your artwork is (and is being printed in) one spot color then sending a grayscale image to print is perfectly ok. You just need to tell the printer which color/ink you want.
You can change the color using Illustrator's Recolor Artwork though:
Create a color group from only the spot color you want to use (Choose "New Color Group..." from the swatches panel dropdown menu with the spot color swatch selected).
Select all your artwork and hit the Recolor Artwork button (or Edit → Edit Colors → Recolor Artwork...)
Select the color group you created in the color groups list on the right.
Change the colorization method to "Scale Tints". Either do this from the dropdown under the "New" column or in the "Color Reduction Options" next to the preset dropdown.
Another option is to use your grayscale artwork as an opacity mask on a solid spot color base:
Group all your artwork and duplicate the group.
Set the bottom (as in layer order) group to a solid fill of your chosen spot color.
With both groups selected hit the "Make Mask" button in the Transparency panel:
- Invert your mask:
- You can use the Flatten Transparency (Object → Flatten Transparency...) to "Apply" your mask.
Note that whatever method I use there is always some discrepancy in the tint values (sometimes only .1 or .2, sometimes 1 or 2 but there is always some change). If you're concerned with exact values it may be better to use these methods as a preview but send the pure grayscale version to print.