I am looking for webhost/mailserver host whose smtp I can use for my other email address (with different domains, on other hosts). It's okay if they ask me to check my email first before they allow my IP address to send mail using a different email address.

(And no, I am not a spammer. It's an idiosyncrasy on my part.)

I hope someone can point me somewhere. Thanks in advance.

Most hosts can do that however they'll probably need to set it up so that their mailserver will also relay email for those domain names. Since this is not a feature often requested they will not have it listed under their "features"

You'll have to ask them this as a sales question before signing up. Make sure they actually UNDERSTAND what you are asking :)

People are so easily tempted to say "yes we can do that for you" to every question you ask just to get your business.