I got a Masterlock U-shaped bike lock...much harder to cut.
I lock my hand-truck to a railing, next to the 20+ other locked up hand-trucks.
Tell the center manager you can't leave until you have a hand-truck. When he says, "aw, come on, you're on a house-call route, you don't need one", refer to the PCM you've just recently had about the proper way to load an over-70 onto a hand-truck.
Refer to the Eight keys: Get an object in your POWER-ZONE! (Hard to do with a 4'x6' 120lb PBTeen bed getup)... Use existing equipment...(hard to do if you don't have said equipment), etc.
Refer to the 5 keys to avoiding slips and falls...kind of hard to scan your walk area when you're carrying a stack of amazon/zappos packages up the rich ladies' awesome curving stone staircase...
If you want to 'take it to the streets', message the center (every time) that you need help with an over-70 and the consignee isn't home...someone's going to have to break off and help you...rinse, repeat.
Bring it all back to safety, and throw in some efficiency arguments if you want to get fancy, but your center manager needs to get you a hand-truck.
(and when you get one, lock it up with a good lock...)