I am not a Hamachi user, but I would think you could change the service to manual instead of automatic. A look at services may give you a start.
Next I suppose that when you start Hamachi its going to connect the last connected, but since you are then in control you can switch it then.
If it does not start after executing the app then write a batch to start or stop. Or, enable and disable the network adapter as example
$wmi = Get-WmiObject -Class Win32_NetworkAdapter -filter "Name LIKE '%Hamachi%'"
$wmi.disable()
–or–
$wmi = Get-WmiObject -Class Win32_NetworkAdapter -filter "Name LIKE '%Hamachi%'"
$wmi.enable()
Keep in mind that when calling a method in Windows PowerShell, the parenthesis are required.
A script with a chooser option would do nicely.