Hi Peter,
You're right, that isn't right. What you need is the infamous dual diameter heater hose. It is molded with two sizes. When I bought my car, it had some rig where two hoses where clamped together with a coupling. Somewhere down the line, I found it needed this special hose. Needless to say, I now have the correct hose now. For my car 111024, the # is 111 831 00 94. Hopefully yours is the same.
BTW, the bypass is working very well and one day, I will dive in and replace the cores. I have two brand new ones collecting dust waiting for that day.
Have fun!