I do this all the time.
Bring a laptop, make sure there's wifi. Whack everything in Lightroom, make basic adjustments and export the images. You'll need a system to work out which photo goes to which person in the case of headshots, or maybe have an online gallery where anyone can visit and just download the image. It needn't by pretty, it'll just need to work given the time constraints. Maybe a google drive would do it, then all you need to do is share the link.