I think it is very difficult to get a wiki page deleted. There is no "Request for deletion" button, and I fear nobody with administrative rights will read the discussion pages.
I'd add a remark at the top of the old page that it is outdated and provide a link to the new page.
Everybody with a wiki account is allowed to modify any page (well, maybe a few of them are locked, I don't know). Of course, you should not abuse this possibility. I see often that people add categorization to my own pages, add additonional details or fix typos, and I am grateful for this.