Delurking for a moment 
Karen - I would go by the ClearBlue so count last night's OPK as negative. So you can assume your surge started sometime during the night.
I did my first few IUIs early in the window, at around 20 hours. My most recent IUI I got my positive OPK at 3am which left me in a complete quandary as to whether to have my IUI at 5pm that day (14 hours) or 10am the following morning (31 hours). After much deliberating and research I went for the next morning and it led to my most successful attempt yet (all other attempts got BFPs that didn't hang around).
Following that, I started to wonder and did more research and found a study that showed that pregnancies had a slightly higher success rate at leading to a successful pregnancy (so not just the BFP, but maintaining the pregnancy) for IUIs done between around 24 and 36 hours (or something like that) than those done earlier or later in the 12–40 hour window sometimes stated.
So based on my experience, if I were in the same situation again I would go for the next day (so tomorrow) but as early as possible in the morning.