Fastest way to allow sendmail relay through smarthost?

You have specified answer in the question itself. You can do that using

define(`SMART_HOST', `smtp.your.provider')dnl

Are you facing any problem using this. After editing /etc/mail/sendmail.mc you should go to directory /etc/mail. Type make and then restart sendmail service for changes to take effect. Then send a test mail and see message headers (Received:) to see if configuration worked.

If you aren't doing anything more fancy with the cumbersome beast that is Sendmail then you could consider using SSMTP instead.

It's a relay-only MTA which is lightweight and couldn't be simpler to configure.

Do yourself a huge favour and replace sendmail with either a modern mta like postfix or something more lightweight like ssmtp. I'm amzed that sendmail is still used voluntarily