You can add a reminder then and recipient. That should work, however wont if you want it within the process.
I don't think you can send an email to an external recipient just as a text address. The person has to be registered in LANDesk. The closest standatd approach I've got is to use the ADD CC feature which sends a copy of any email updates sent to raise user to another adress and this can be just a textual email address.
It's a common request and I'd raise an ER for it.
I have been able to use an alternative email address field on an incident to send email to a different email account than that of record for a user.
you have to set up the CC recipient functionality (see admin manual). After CC is set up, I placed an auto action in my process, right after the starting status, using the cc recip action. I then use a calculation to fill in the field where the alt email field from the incident is the email field on the cc window.
static def GetAttributeValue(_IncidentCCRecipient):
Value = _IncidentCCRecipient.Process._AltEmail
This will send email to the address on record and the alternate field I have on the window.