If I move files to a new disk will Time Machine do a full backup?
Timemachine identifies backups by the disk's UUID. Therefore, the answer is yes. TM will make a new backup of your files and delete old backups if there is not enough space to hold both copies. 

You could delete the previous backup of your iPhoto library and then simply do a new backup. However, you will lose your backup history.

I did something similar a few years ago and I remember that I was able to point TM to the new directory and, therefore, avoid a redundant backup of these files. Unfortunately, I am not entirely sure how I achieved that. This article should get you started with the tmutil utility, which may have the capability to do that.

A final note as you seem to care about your data. You should not rely on one single Timemachine backup. Especially, if you are going to experiment with sudo and tmutil. After some bad experiences, I maintain two rotating TimeMachine backup disk plus a irregular full copy on a third disk.