I think that you will find the Telldus stick IS compatible with the Bye Bye Standbye 2011 product.
I bought one before I saw your post asking about it so I thought I had bought a lemon ...
However if you follow the instructions on the ByeBye Standby web site for pairing the ByeByeStandby 2011 with a classic controller it also works with the Telldus stick.http://www.byebyestandby.com/how-to-use ... -range.php
All you do is:
Select new item - "ByeByeStandby code switch" in Telldus Control Centre
Pick a code e.g. 4 c
Press the off button on the 2011 device release then press and hold it until the blue light flashes once a second to show it is in learning mode
Click the off icon on the Telldus Centre