Recover Photos from Backup

I would like to recover the photos in the Photos folder of a Mac backup and make them available to one, and ideally two, MacBook Airs. What options do I have?

My Mac died. I bought a MacBook Air to replace it but needed to do so quickly, so opted for one with the regular amount of storage. This wasn't enough to copy over the Photos folder of the Mac backup I had, so this folder remains on the external drive I used for backups. Can I access the photos if I plug this external drive into one of my two MacBook Airs? Should I try to copy it to a new external drive and, if so, how can I do this given that neither MacBook Air can accommodate the size of the folder? Should I consider some sort of network drive but, again, how can I populate it? Or a cloud solution might be best but, again, how can I get the photos off the external drive and onto the device or service I choose?

Thank you in advance for any guidance you can offer me.