> I cut my hand on the fall, and the blood had me worried because both rangers had warned of recent lion spottings.

The Mt Whitney area doesn't have the mountain lion issue. So hiking alone is probably much safer, in that respect. A hiker who is bleeding and injured in mountain lion territory is in much greater danger being alone than if accompanied by another hiker.

You can hike alone on the Mt Whitney trail, and not need to worry about mountain lions. ...but watch out for those killer grouse! grin