7aH gel cells seem light enough to carry,
A 7Ah gel weighs 5 pounds. Consider you would need a charger for the gel cell, which is added weight and bulk.
An Astron SS-50, 40 amp supply only weighs 5 pounds. A 12~15V supply big enough to run a QRP rig like the 817 would be smaller and lighter than the charger for the laptop and certainly lighter and more compact than a gel cell plus charger.