@ Philo
I don't believe it is a matter of exclusion/detection of snoopstick elements, but one of conflict. If you have both snoopstick and the web shield enabled then you have no internet connection, remove one or the other and no conflict and internet connection is restored. You aren't actually getting alerts about the snoopstick software are you ?
If avast is alerting - What we need are the file names and locations of of any avast detections relating to this ?
This leads me to believe that snoopstick also uses a proxy to achieve whatever it is that it is supposed to do (I know nothing of this program), so if it uses a proxy then you need to a) find out what that proxy port is and b) coordinate it with the web shield proxy.
You would do this by adding it to the redirect ports and unchecking the Ignore local communication, avastUI, Settings, Troubleshooting, Redirect settings, HTTP port(s): see image example, add the port after the 80 and must be separated by a comma, where xxx is the snoopstick proxy port number.
However, there is obsoletely no way I would consider disabling the web shield as snoopstick doesn't provide the same protection, it isn't looking for the same things.
The web shield can block exploits and links to malicious scripts that could well infect your system, this is more beneficial as it is capable of blocking said malicious scripts and links without having to know exactly what malware is on the other end. In other words it could be blocking malware that may not have been detected by the avast signatures, etc. This could account for the infections you spoke of.