When you convert from RGB to cmyk as mentioned above you will most likely need to do some color correcting. Your best and safest bet is to convert that image to a CMYK bitmap and publish / print the file to a PDF. Make sure your PDF settings preserve the CMYK image and send that to your client for proofing purposes.
As many have mentioned your monitor will show RGB and most programs will give you a gamut preview of colors when converted to cmyk. If your monitor is NOT calibrated correctly guarantee your colors will be off no matter what. If your printers is not calibrated correctly with your software and monitor your are even more off color wise.
