In the 70's I started to see ads for a starter with pre lube pump built on for heavy equipment and truck diesels but I never had experience with one.
Basically it was a Delco type,solenoid engaged starter with a oil pump on the commutator end plate.
The solenoid had been divorced from the starter motor circuit so operating the start switch first started the starter motor/pump turning,when oil pressure developed a pressure switch energized the solenoid, engaging the pinion gear.I don't know how this was done while protecting the starter gears.
I have never seen a small, inexpensive preoiler pump advertised for our smaller engines.
I remember seeing somewhere described an accumulator type system for engines that charged and trapped oil in an accumulator while the engine was running that could be then admitted to the system later for pre lube.
Dont worry about that little chevy, she'll be fine--just turn the key, count to 20 and turn her loose.