Softwood is from coniferous trees, in animal bedding it is usually pine and cedar etc..., which is generally is recommended to avoid. Aspen is a hardwood.
However, you don't have to use aspen that specifically says "snake" on it. Aspen is aspen. The "snake" stuff in pet stores tends to cost way more than it should, and comes in smaller bags usually. You can try the small animal department for a larger and less expensive bag of aspen. I get my aspen in the equine department of a farm supply store. It is intended as horse bedding. 45 pounds for $5. Just make sure it is 100% aspen.