Can you export (save-as) the model to somewhere it can be read by the other machine? Maybe 'pack and go'? You could also zip the directory you have all your files in for the model and transfer that to the other PC and unzip it, then run the study. It should take everything you need along with the file I would think.
Is the file your running a static simulation on a part file used ? or a number of different parts thrown into an assembly that will end up being welded?
Copy the file of your weldment profiles to a shared drive and then have your coworker add the file location for Weldment Profiles under system options on his machine. If the model (and its child components if an assembly) is/are in a shared location he should be able to open it and run the simulation you need