Hello Michael,
You are right about that the installation is checking a registry key (HKLM\SYSTEM\CurrentControlSet\Control\ProductOptions), but we can't avoid that so easily. However, I managed to install the personal edition.
1.
Download and
Run the installer downloaded from
http://www.teamviewer.com/. On the
Welcome page click
Next, directly after that at the
Environment page click
Back.
2. Leave the installation window open and start
Windows Explorer. Now go to your temp directory by typing
%tmp% into the location bar.
3. Go to the Detailed view (View -> Details), and sort at the
Date modified column.
4. Open the
nsxXXXX.tmp directory (where the Xes are some random characters/numbers) and open the environment.ini file with Notepad.
5. Change the value of
Flags= of
Field 1, 2 and 3 from
DISABLED into
GROUP|NOTIFY so you have
Flags=GROUP|NOTIFY.
6. Change the value of
State= of
Field 1 into
0 and the value of
State= of
Field 2 into
1.
7.
Save and close the file. Now right click the
environment.ini file, choose
Properties, check the
Read-only flag and click
OK to save the change.
8. Maximize your installation window again and click
Next to go to the screen where you can now choose the personal version!

Maybe there is a quicker way, but at least this works.
Good luck!