the  thing about converting it to cmyk is that converts using your settings not the printer's settings.

perceptual coulours on the monitor can be difficult to match printed output - i think it's near impossible - i doubt you get paper as white as your monitor - nor could you print 'black' as black as you monitor looks like turned off - monitors and printers use a diffent gammut, thus you will have to use a colour, or two, that is allready printed for your logo colour-