Norway to Silver Peak is entirely reasonable and looks like it could be a lot of fun. In my mid-teens I hiked from the north shore of the east end of Carlyle Lake to Silver Peak (we used to spend summers at my family's camp on Carlyle). It was bushwacking in the general direction of Green Lake then to Bunnyrabbit Lake before picking up the trail and following that to Silver Peak. I was by myself with a map and a compass (no GPS at the time) and I remember it not being an overly long nor difficult hike - I was there and back in a day which was a much faster option than our usual Silver Peak route which was to camp at Clearsilver and hike up the next day.
Norway to SP would be much more direct and shorter than my start at Carlyle and I think bushwacking would be faster than meeting up with the trail. Maybe you could work your way along the north shore of Norway then along Sandy before a more or less straight shot north to the peak? Having Norway and Sandy as reference points for the first 1/3 to 1/2 of the hike would be useful but sticking to the shoreline may be more bush than if you went straight up away from Norway.
Yes, a GPS app would be a helpful backup to a paper map and compass and also a nice way to confirm your position and view your progress. I use and really like the free OsmAnd app for my backcountry, out of cell range mapping. (The app is free but I did eventually pay the $2 for the contour lines add-on - especially helpful for route-finding on scrambles out here in BC.) I've got offline maps downloaded to my phone and can get multiple days of battery life with my phone in airplane mode and turning GPS on to locate myself as needed. That said, it would be a good idea to bring along a portable power bank as backup. The nice thing about OsmAnd is that it uses the OpenStreetMap maps, so you can always preview the map on your computer at
https://www.openstreetmap.org.
For route planning, I've found
https://caltopo.com/ to be quite useful. You can overlay many different layers on the map (for example: contour lines, slope angle shading) and trace out a planned route. Once you have a route drawn, CalTopo can generate an elevation profile for the route and you can also export the planned route as a .gpx file to load into your OsmAnd app to follow out in the bush.
Have fun planning!