Great question! I think the traditional denominations are anal about this sort of thing. I once listened to a sermon where the pastor stated that just because Jesus was sinless does not mean he did everything perfectly, such as always cutting the proper angle of wood as a carpenter. I relate to a human Jesus and I never relate more to him more than when he angrily overthrew tables at the temple.
To your point, sin is non-transferrable. This applies to you, me and Jesus. The capacity to sin is human. This potential need not be realized at every turn. You and I do not realize this capacity every chance we get. Sometimes you and I get it right. Of course, it is those other times that we need help.
I believe most of the times I sin, it is driven by ego. The most basic human ego is depicted in the fall, the desire to be God. This translation opened my eyes to this basic human desire to be God.
When all of the other gods
have come together,
the LORD God judges them
Psalm 82:1 (CEV)
Okay, but then if you're saying that sin is a part of human nature that's sort of like saying that Jesus wasn't human and He was human just as much as He is and was God. However, I do agree with what you said on the part about how it's possible to make mistakes without sinning and in that sense I always believed that Jesus made those kinds of errors and had "brain farts" as a human being like we all do lol I also always wondered if He always knew right from wrong from an infant and small child,.. because when you don't know any better I don't really consider that sinning if you haven't been taught that it's wrong yet.