Could you clarify what other climbing gear you would need for snow climbing? I would say that crampons go hand in hand with an ice axe. I totally agree with you that these 2 tools are completely necessary for climbing hard spring and summer snow, however I disagree that it is necessary or even a good idea to first climb summer snow that you are planning on skiing.
I agree that it is very important to know what the snow conditions you will be skiing are like before dropping in, but I don't think a long snow climb is necessary to do this. Spring is different, when conditions are changing dramatically day to day as the snow compacts, but by mid summer (when the Rollins Pass road will be open), the snowpack should have transitioned to firn, meaning that although afternoon surface slides are possible, the deep snowpack should be locked down. Also, checking small representative, but lower consequence snowfields in the area should provide insight into what is happening on the snow surface. Also, snow climbing is a skill of its own, and not something that should be attempted for the first time in late summer because self arresting is very difficult. But if one is going to ski Skyscraper they should realize that it is a steep line that ends in rocks, and that if you fall on summer snow you will accelerate very quickly! I think soderfunk was probably also getting at this. Please let me know what you think about this soderfunk.
But, if one isn't up for skiing a steep, high consequence line like this, Rollins Pass has the King Lake bowl which is even closer to the parking lot, has a trail that you can hike back up right next to it, and has a nice long run out so there is no concern for sliding into rocks. It also has a real fun cornice to jump off of at the top. If you are thinking about skiing Skyscraper I would recommend checking this out first.
A couple pics of King Lake Bowl:
