I think the HP 45's you buy from HP are dye based, however I know that some wide format printers use specialized 45 carts that use a dye/pigment hybrid.
I believe that the HP 45 cartridge uses pigment ink. My old workhorse HP 712 used 45 (black) and 23 (3 color) cartridges with something like 40 cc in the 45. Easy to refill and huge capacity.
I don't know why you would want to dilute that with dye because you will give up the smear resistance of it, but, many suppliers of inks already dilute their so-called pigment black ink with dye because it is cheaper for them. You can easily tell if an ink is 100% pigment by smearing some on a piece of paper with a Q-tip and, after it dries, let water drip across it to see if it runs.