As a former electrician I can confirm a shop vac works well to install pull string.
In my experience a simple plastic grocery bag is the best. My boss had bought several sets of Greenlee pulling plugs for various conduit sizes but after trying them multiple times we went back to the bags. If one isn't enough use a bigger bag or two or more.
It works either blowing or vacuum, in my experience using vacuum was more reliable. We have at times done both in tandem.
(Then there was the time the farmer/customer installed the conduit himself to "save money"... We ended up using his vacuum manure tank... Not a good day...)
I don't know what the pup tongue looks like internally but if there are other hoses, wires, etc a shop vac is unlikely to work.