Best way I can think of doing this would be to create your own little batch file that silently uses the FOR construct. For instance, you could create a batch named BatchSet.bat, stored somewhere on your path. The batch would contain the following code:
@Echo off
for /f "delims=" %%i in ('%2') do set %1=%%i
Set %1
If you run this with the following command:
BatchSet MyVar whoami
You'll get something like:
MyVar=servername\John
Obviously, the command you run should limit its output to a single line to be stored properly in the environment variable.
For instance, if you run it like this:
BatchSet MyVar Vol
Then you'll only get the first line of the Vol command's output
MyVar= Volume on drive C is labeled MyDisk
But all in all, it's a fairly elegant way of doing what you were looking for.
Note that the last line in the batch is simply there to provide visual output. It can be removed altogether.