Is this not a valid question or is this forum for vendors only?
I have no idea if any third party ink for my HP will be smudge proof the factory HP 45 & 23 ink can be trashed with a single sneeze one day or one year after printing.
So far I can find only this forum and one other and can not find any info on replacement ink for my printer.
I'll bet that you are printing on a "swellable" paper. HP recommends these papers because they have better longevity than the faster drying/non-smudging nanoporous papers (also called microporous). Here is a link that discusses the various types of paper (Ilford uses the term "resin coated" instead of "swellable") (http://www.ilford.com/html/us_english/prod_html/galerie/htm/gtp/how_suits.htm).
Your problem is a common complaint of those who use HP's archival inks and papers. As a test, drop some water on one of your prints and let it set for 20 seconds. Does the surface feel slimy and the ink move when you slide your finger across the surface? If so, your paper is swellable (many of these papers use a gelatin-like coating). Do you really need archival prints, or is a 10-20 year life sufficient? If it is, try any of the common "fast drying" papers.
Thank you for replying I was afraid this post was in the wrong place.
I have all ways used HP inkjet cheap paper because I do not print photos.
What I am trying to find out is can I buy ink that will be smudge resistant (for my HP) like Epson and Cannon ink.
I can go to Office Depot and print on plain paper and the next day the Cannon and Epson prints will not smudge like the HP copies.