It's not so tricky.

The first one to start updates the list of files to be actioned, sets a flag in registry or ini file to say it is busy, and then prompts the user.

The next one to starts checks the registry, sees that there is already a user prompt open so just adds the file name to the list of files to be actioned and exits.

When the user responds to the prompt the first process gets the list of all the files to action and deals with them.