Trigger a smart campaign by form submission on a non-Marketo landing page

I don't think you can trigger off a non-marketo form in any reliable fashion that covers both new, known and unknown leads.

You might be able to trigger off a "clidks link on web page" using the link on the submit button--but it would only work for known leads.  If the button is embedeed in the form, you may need to add the Munchkin to the post-form landing pages for each form, then trigger off "visits web page".  Again, the problem with this approach would be if someone forwards the email, or the page is visited by an unknonw lead, you wouldn't have the email address to which to send the post-form email message.

If you can convince the client to use Marketo landing pages and/or forms, you can either create a webhook or use the API interconnection to send the collected data  back into their system 

I've successfully used webhooks to collect webinar registration data in Marketo, then post directly to our client's webinar provider.  You'll have to get the format of their HTTP POST, then incorporate your tokens for the appropriate fields. 

For ON24, the webhook looks something like this:
http://event.on24.com/utilApp/r?eventid=xxxxxx&sessionid=1&key=xxxxxxxxxxxxxxxxxxxxxxxxxxxx&job_title={{lead.Job Title}}&firstname={{lead.First Name}}&lastname={{lead.Last Name}}&email={{lead.Email Address}}