Can I try to ping a website through a specific adapter?

The ping command will allow strict source routing so you can specify the default gateway to use on the way out. (This assumes your interfaces have distinct gateways i.e. are on different networks)

ping -k 192.169.1.1 microsoft.com        ^ default gateway for desired interface

Using WMI Win32_PingStatus you can do the same thing where you specify SourceRoute and SourceRouteType (This is essentially the same as using ping -k)

Alternatively:

If your network interfaces are on the same network, like a LAN card and a wireless adapateryou can add a custom ROUTE to your machine, which can send all traffic through a specific interface.

From ROUTE HELP:

route ADD 207.46.0.0 MASK 255.255.0.0  192.168.1.1 METRIC 3 IF 2        destination^      ^mask        ^gateway     metric^    ^                                                      Interface^

ping also has an option in Windows:

-S srcaddr     Source address to use.

So you can do something like

ping 10.10.10.1 -l 0 -S 192.168.1.1

where 10.10.10.1 is the destination address and 192.168.1.1 is the address of the source adapter