I want to change the default python version I use, without affecting any other defaults. Appending the python path to the $PATH environment variable only accomplishes that as long as there is only the python executable at that given location, which is not the case if I want to use the /usr/bin version (export PATH=\usr\bin:$PATH). 
I know I could theoretically create a symbolic link in some other folder of my choosing, but this is not very elegant.
Is there any other way of changing the default python (like a nice environment variable that python uses which takes precedence over the $PATH environment variable)?
In general, Python itself does not provide any way to do this. Once Python starts up, there is already one particular version running, and it can't change to a different version on the fly.
Your operating system may provide some way of choosing which version of Python is the default (e.g. eselect python on Gentoo Linux), but it's impossible to say whether that's the case for you without knowing what OS you're using. If your OS doesn't provide something like this, it is possible to make your own scripts to set and change a default Python version.
Changing the default python without changing the $PATH variable?