Also as Yer_Man suggested, all of your pictures on your Mac are exactly the same as your pictures at iCloud. If you have "Optimize Storage" turned on in Photos' Settings to save storage space on your device, then Photos may store only smaller images on the device and rely on iCloud to keep the full sized images. This is great, since with the lower resolution images you can scan through pictures very quickly, and they look great on the screen. And, if Optimize is chosen, and you want to edit or crop a picture, Photos will reach out to iCloud to get a full sized image for you to work with. It's the same for editing or printing or anything that demands the full picture. Your optimized Library may take up less than 20% of the space of a fully downloaded Library. On my iPhone, Photos takes up way less than 10% of the space it uses at iCloud.
I said, "Photos may store only smaller images." When you need a full sized image and it downloads to your device, it may stay local until it sees that space is needed. You can't predict just how much storage will be used for Photos on any given day-- it can fluctuate a bunch.
Perhaps the biggest downside of "Optimize" is that backups may not include all your full files. I don't do "Optimize" on my Mac, because I want to be able to do backups. I use it on my iPhone which has way less storage, and I rely on the Mac for backups.
As Yer_Man says, you can keep the full Photos Library on an external drive, as long as it is formatted properly, and indicated in the link I'll repeat:
Move your Photos library to save space on your Mac - Apple Support (IE)
If you're confident that your Library is working well, then you can just drag it from the Pictures folder to your external drive. You'll have to designate this new Library as you System Library in Photos' Settings>General, and connect it to iCloud in Photos' Settings>iCloud. It may take some back and forth with iCloud to settle down
