I guided for pike in northern Sask, and have fished all over northern MB and NWT for big pike. All of the aforementioned information is gold. Don't forget dahlberg divers. I would recommend some of the knotable wire (like tyger) for leaders, or you can buy the cheap nylon coated multistrand wire and bring a lighter to twist and melt for each time you switch out. If you are not sure how to do this, i'm sure there are youtube videos explaining it. Especially for poppers, a lighter wire for leaders is useful, 15lb or at most 20 to prevent the fly from sinking, but the fish wont be leader shy and for sinking flies you can get away with whatever length and strength wire you like.
Your 10 wt will be great for casting large flies, but overkill for most of the fish. Some of the pike that you are fishing over will certainly be in the 20lb in june, and will be worthy adversaries for your 10wt. That said, Most will be ten pounds or less. If you can manage to bring a 7 or an 8 wt for tossing smaller flies, your arm will thank you. While some like to throw absolutely enormous flies for pike, 5-6 inch streamers are plenty large, and will land more softly, spooking fewer of the fish.
While pike have the reputation for being voracious, and it is certainly deserved, often they are not. Its very common to see some of the largest fish sunning themselves in very shallow water after a big meal, and they wont be as aggressive. A 5 inch bunny leech in black or yellow, laid softly within a few feet of them and slowly stripped is much more effective than ripping an enormous 10 inch long musky fly past their heads in those circumstances. For that kind of fishing, an 8 wt would be preferable but it is absolutely not necessary, and if you are on a budget, I would prioritize other items, like good material for making wire leaders, jaw spreaders, long pliers, bug spray, and simms sun gloves ( with the stripping finger) over setting up the other fly rod. That said, if you can swing an extra fly line, it's always good to have two setups in the boat (one surface, one subsurface)- it would be worth your while.
If you have a 5 or 6 weight with a sinking line, consider bringing it for walleye, with some clousers and conehead buggers, because let's be honest, those things are delicious.
As said before, your timing in june is excellent for big northerns, be sure to bring AT LEAST one pair of good polarized sunglasses because many of my largest fish while guiding were sight fished to during that time of year. Try to focus your efforts of dark bottom bays, bays with a northern shoreline and good southern exposure, bays with creeks flowing into them from smaller dark ponds, and river mouths. By end of june you may start to see some early weed growth, and pike will certainly be gravitating to that as well. It will depend largely on the timing of the ice out, but in the case of a late ice out, focus on the bays described, otherwise look for any weed growth.
Will you be on big sand lake or some of the smaller lakes along the s seal river circuit?