I know this is old, but none of the answers here is a real solution if you want to be able to double-click Python files and have the correct interpreter used without modifying your PYTHONPATH or PATH every time you want to use a different interpreter. Sure, from the command line, activate my-environment works, but OP specifically asked about double-clicking.
In this case, the correct thing to do is use the Python launcher for Windows. Then, all you have to do is add #! path\to\interpreter\python.exe to the top of your script. Unfortunately, although the launcher comes standard with Python 3.3+, it is not included with Anaconda (see Python & Windows: Where is the python launcher?), and the simplest thing to do is to install it separately from here.