It may work, distance is hopefully short enough that the stranded won't affect it. My reference books are all in the car my wife drove today so I can't look up the specifics on derating with stranded cable. The proper way would be to run solid core cable to jacks on either end, then patch cables at the end. Also, if the ends of a patch cable have problems, you are then stuck trying to put connectors on a stranded cable, which is a recipe for ruhroh.
If you do go with Cat-6, don't put the excess into a tight service loop, leave it as loose as you can and not very neat.
You might want to hold out and see what the new version of WHS will be like before buying one--or building your own so you can change it when you want, not waiting for HP to deliver an update (if ever). You could check into virtualizing it then...along with a firewall/gateway/router distro 😉