This has happened to me a few times. I sometimes have long gaps between seeing WG's and prices can fluctuate. I always go in with the 'old rate' cash counted out in one pocket, and a reserve stash in my wallet just incase. To date i've never been refused paying the old rate!
On a couple of occasions, i've genuinely misread the price or done a little shopping pre-punt and arrived with insufficient funds - and on those occasions, I was allowed to stay, one at a slightly reduced time (1hr down to 45 mins) but we ended up having fun and I stayed the hour. The other said don't worry about the extra money
Not identical to your situation but I have found WG's to be more flexible than I expected on price. That's not to say you turn up with half the agreed fee and expect double time, but its hard to turn away a polite punter who is 20 notes short so I don't see any problems in your case.