If you are riding
, then it's not the rainy season in Alaska that you have to worry about, but the inland weather along the Alaska highway. While the coastline tends to be temperate but wet, inland you'll have to cope with a continental climate. In that regard, conditions inland will be closer to what you could expect in Fairbanks, for example.
In a nutshell, if you ride the Alaska highway, you'll get some wet weather, including maybe some torrential rains and maybe snowfalls, but you are also likely to have sunny and maybe warm days. The Cassiar highway (highway 37) will probably be wetter. But while you may find some average data on Environment Canada
's system (check for Whitehorse, Watson Lake for Yukon, then Fort St. John and Dawson City), the problem is that you'll either have gorgeous weather... or snowstorms. On the plus side, if you stay on the Alaska highway, you might be able to get the forecasts and decide 2-3 days ahead of time if it's wiser to wait or ride.
With all the cautions about averages, I would say that daytime temperatures could be very decent, maybe even warm, but nights will get cool if not cold. This means you need to get ready for serious-weather camping.
Daylight-wise, when I travelled there many many ears ago (by car), I felt that August was the worst month for travelling. People have been abusing all the daylight available and drove like zombies. As days shorten in August (to a nice 16 hours/day in mid August), people start sleeping again at night and they drive much better by the end of August and in September. Of course, when it's Sept. 21st, there is 12 hours of daylight, typically from about 8:30 a.m to 8:30 p.m.