No 'correct' prodedure per se. Some labs deamnd sRGB and will convert to the output color space when they get the file. Others will allow you to convert to a supplied profile. This IS preferable as you can soft proof using that profile and convert and send.
Using a profile for soft proofing but not using to convert is problematic; what rendering intent will be used, why can't you convert and post edit? So, IMHO, either find a lab that is fully color manged (not easy) or just buckle down and send them sRGB which isn't ideal but all they allow.
Author “Color Management for Photographers" & "Photoshop CC Color Management" (pluralsight.com)