How many pages is your document?
If you are giving your customer a PDF, you can convert it to gray scale directly in Acrobat--assuming you have Acrobat.
I wanted to add something. I was assuming that you are on a MAC. On a PC and with Acrobat/Distiller installed, this is a simple task by simply printing to a PS print driver and distilling the .ps file. This is where Dov Issacs is beginning to cringe.
I dig up a thread I remember reading for Mac users:
Take care, Mike
Printing to .ps (or directly to PDF, which automates the .ps to distiller part on Windows), is the only way you will get composite gray directly from InDesign CS5, but it isn't foolproof. Make sure you have your Appearance of Black preference set to Output All Blacks as Rich Black or you'll wind up with dark gray screened type and other 0,0,0,100 elements. When you output blacks accurately during a conversion, 100% black is reserved for 4-color rich blacks.
If you need to continue working on the document—not simply convert it—here's a script for OSX that converts the document colors and placed images:
There's also this .js script and blog post from Harbs: