Not sure what the laws are in Multnomah, but I would rather have it legal and completed than to have an easement. An easement could cause you trouble down the road. Either way you go, make sure it is legally documented.
Look at it this way....presently, you don't have a problem. On the other hand, your neighbor has an issue he'd like to resolve by having you make a concession that could come back and "bite you" in the future. You are correct assuming that if done the wrong way, this issue will become an even bigger problem when it comes to changing ownership in the future.
My recommendation is that both parties sit down with an attorney to review your options. The last think you should do is just to move the fence without first understanding what's involved. If you are going to do it...do it right!
Or........he you could grant him the easement that runs with the owner and not the land. However, you would still want that to be surveyed and done on a legal document and on record. (Need to confirm with attorney on this.)
Either way, this is going to cost somebody a little money to accomplish if you want to protect yourself and your land. It is very admirable of you to want to help out your neighbor, but having been in this business for quite a few years, I can almost assure you that unless you do this by legal means, an issue will almost certainly arise down the road.
Do yourself and your neighbor a favor and get it done right the first time.
One option is to create an easement for your neighbor. This way, you're granting him the right to use the strip of land but not transferring the right of ownership to him.
A more formal option is to perform a lot line adjustment. You'll need to get a surveyor to generate a new plat map and record the new lot line with the county. The cost for both will probably run you about $5-10K. This keeps the property lines clear and doesn't present any complications on any future sales.