An engine swap is probably a major modification, unless both the new and old are the same manufacturer and the same horsepower. Even with the same manufacturer and horsepower there may be cases where you are still looking at a major modification, but most likely not. A prop swap is also probably a major mod unless the change is very minor. If there is any doubt you can run it past your local FSDO.
Assuming you are doing a major modification, your first point of reference is your Operating Limitations. That will tell you what you need to do. In most cases you will need to contact the local FSDO and tell them what you did. They will then assign you a flight test area and duration, which will put you pack into Phase I flight test mode. Once the modification is complete you should record the work in the aircraft logbook. After you fly off the test hours you will need to make another logbook entry stating that Phase I testing is complete. See the language used at the completion of your original Phase I testing for an example. I believe it can also be found in AC20-27G.
Weight and balance paperwork will also need to be updated. This should be done before your Phase I flight testing begins. You can reweigh the plane or just do it on paper by subtracting the weights and moments of the old components and adding the weight and moments of the new components.
You do not need to hold the repairmans certificate to do this work or sign it off. But if you do not hold the repair. cert. you will need to have enough documentation to convince an A&P that what you did was sound and airworthy.