Jürgen, there is some good information at this link [CLICK]. But basically, we need to intercept the data that is going from your PWS to WU and send it to a locally running OS Weather Service instead.
I am note sure if the Synology NAS will run NodeJS. This is the underlying platform of the Weather Service and a key dependency. If it does then that would make a good host for the local Weather Service. If not then you could use a cheap raspberry pi (there are instructions in the link above that detail how to get Weather Service running on a raspberry pi).
The next step is to “intercept” the weather data and get it redirected to Synology. How to do this depends on your network setup. Some wifi routers let you setup an “intercept” but most telco provided routers do not. So let me know the make/model of your wifi router and we can go from there.