Cyan really isn't used in B&W printing because it's just a density filter - you'll just end up increasing printing times. What you need is more magenta in multigrade printing to increase contrast but, really, it's probably not going to help. Years ago, Kodak made some B&W paper specifically for printing from colour negatives but no more.
If you want to do B&W printing at home without developing your own negatives, you need to use either Ilford's XP2 or Fuji's CN B&W films. Both have clear film bases instead of the orange mask but are still C-41 process films.