Schwarzee to Hornli Hut is a great acclimation hike, but better still to hike from Zermatt. It will also give you a good look at the climb during daylite, I climbed up on it for aways the day prior.
I also hiked solo and came from sea level to the Matterhorn Climb this month and I hiked Oberrothorn 3415, nice training hike, A local favorite! I also hiked up to the Gandegghutte 3029 and stayed overnite to help acclimate. lots of the guided groups heading for the Breithorn were starting the hike to this hutte from the Furi tram.
I used a local guide for the Matterhorn, and be ready to just keep moving... Lots of training hikes right from Zermatt.
When you practice hike...just pump it as steady as you can for longer periods as you acclimate...it's a lot of elevation! I can't wait to get back and finish it!!