We do mostly driving , a few short hilkes but nothing extreme. No skiing for us either.
In April, it would be skiing or snowshoeing. For what you describe, May or very early June would be better. Fall would have more hiking options, but snow can start in late Sept.
I've been there multiple times in May through the first week of June. Sometimes the Chateau Lake Louise was surrounded by snow, and once it was melted out with snow starting partway along the lake. Banff is more likely to have the trails close to town melted out and the trail to Johnston Falls was a conga line since it was one of the few trails hike able. At Yoho, Lake Emerald was either snow or maybe half the trail along the lake melted out. The Icefields Parkway was beautiful, but hikes at various stops were limited by the snow cover. So beautiful driving, though access is limited to the main roads, but limited hiking.
It is a great time for critter viewing with Kootenay NP in the lower river sections especially good for bears etc. The spring trips were mostly utilizing the great deals for the timeshares in eastern BC via AC or the old XYZ program. If you don't mind driving, it's a very doable day trip to do the loop through Kootenay to Lake Louise and out Field. Another trip in early June was a loop through Banff etc and then down to Waterton and then the eastern side of Glacier where we lucked into a room they had just opened for the season; great critter watching at Many glaciers. On that trip, we saw a lot of baby critters of various types.