The PuTTY launcher uses the default ports for SSH. If you need to use a custom port, you can do this by creating a custom launcher.
To create a Custom Launcher, go to Administration | Secret Templates | Configure Launchers.
Create your custom launcher using the process you want to start (this must be in your PATH), then use the right command line parameters for your tool.
The $HOST, $USERNAME, etc. would map to the names of the fields on your Secret Template.
The field HOST on the Secret Template maps to $HOST in the Process Arguments for the custom launcher. (for example: $HOST is the variable to represent the HOST field)
You would then assign this custom launcher to Secrets by going to the Secret Template (Administration | Secret Templates | Pick your Template, then Edit | Configure Launcher.
Create a Secret with the Secret Template and try out the Custom Launcher icon.
The command line parameters for PuTTY are in the PuTTY documentation under 3.8. (-P is for port)