In that case, unless the wax is dirty, it should be fine to cover with storage wax. As spring snow is often dirty snow, hot scraping wouldn't be a bad idea anyway. Unless there is tar or some other substance that won't come out with hot-scraping, skip the cleaner.
Crayon some wax on the edges before you melt it on the bases to ensure you get good edge coverage. It keeps them from rusting. I usually just use the wax I ski on in the early season as storage wax (CH7 most years). That way I just scrape, brush and go. No need for fancy wax in the early season, since your technique needs more work than your tuning after a summer off. I've found really soft wax (CH10) as storage wax tends to pick up whatever happens to be floating around it, which harder waxes tend to be a little more resistant to crud. I store my skis in unzipped ski bags to allow better ventilation while still providing some protection.
I also turn down the bindings to the lowest setting and write the DIN setting, edge angles, and last wax used on a piece of blue painters tape so I don't forget.