Instead of sending the URL of the team project ID, would you be able to publish a separate Axure Share prototype from the team project file, via "Publish > Publish to Axure Share". That'll generate a new URL that's separate from your team project's original ID and detached from any updates resulting from check-ins.
Another option is to manually create a new team project from your existing file. To do that, open your local copy and select "File > Export Team Project to File". When you open the exported RP file, you'll be able to select "Team > Create Team Project from Current File", which will create a new team ID in the target workspace. Your team can then retrieve that new team project to continue working.