Is it possible to use a token in a wait step, not for a specific date, but a program token such as {{my.wait time}} and have the value of that token be a wait value in minutes or days, such as "15 minutes"?
Yes and no.
Rather than directly using the token in the Wait, use a Text {{my.token}} to manage another DateTime field (using date math {{lead.next wait end}} + {{my.wait time}} minutes).
Then Wait until that DT field.