Getting skunked is always a risk but you should be fine. That is pretty much prime time. You may not have as many sockeye by then. If you want them you should go earlier if interested in "greener" fish but otherwise they should be lingering too.
Are you chucking hardware or fly fishing?
I was there for the first time in 2015. It is an amazing place. You can fish the Skeena right in town at the island / park. Lots of good water there. Lots of good water further West up the highway too.
If you want to fish pretty much alone, you can head back East and fish in the special license area for $20 a day. It was worth it to me as I had the river to myself and ended up with my best sockeye...and lots more.
There are some big, big steelhead as well.
Also, you have a lot of other rivers in the area, the Copper, etc. And the Kitimat is driving distance as well. And, you pass right by Smithers and the Bulkley...so good.
A day out of Prince Rupert on the ocean should be a lot of fun as well.
Sockeye from the special area: