So would it work for you, if you disable the automatic opening? And you just manually open PuTTY from WinSCP, whenever you need it? – Ctrl+P

Correct, but I have roughly 100 sites I connect to. Most allow SSH connections, but a couple do not. This is why is would be nice if this could be disabled on a per-site basis.

Not a major issue, but just a nice convenience.

Sorry, I still do not understand.
So you have enabled automatic opening of PuTTY sessions:
https://winscp.net/eng/docs/ui_pref_integration_app
Is that correct?

But some of the servers do not support shell/PuTTY access. Correct?

What do you want WinSCP to do about it?

The error is just a PuTTY session with the message:

Server refused to allocate pty

I do not know what you mean by "automatic sessions".

I work with a few SFTP sites which don't allow SSH sessions.

This opens a PuTTY window which then shows the rejected session. It would be nice to be able to skip the automatic sessions.