I have lost the stick. If not, do third party sticks work instead?
ANT+ is the only way to download data from the Garmin Swim watch. I'm not sure about 3rd party ANT+ sticks, but I believe they should work as long as you get the correct drivers for your OS. Some time ago I even heard about a user who succeded to download activities via ANT+ built into his smartphone. So if your smartphone has ANT+ hardware, then perhaps you could try it this way.