Hmm, I just thought of a way to replace a skill, at least for a little while. It's definitely a ritual though, so it'll take some time.
First, we want to slap on a power, so we need to take ourselves out: 5 shfits.
We want the skill to be at a value of 6, so let's put 6 shifts into the spell for.
Next, we need an ingredient that fits the skill. In the case of Rapport, maybe hair of a siren or a succubus would work nicely. We'll use the free tag on the aspect to power the temporary power.
So that would make it an 11 shift ritual, and you'd need parts of something that would boost your rapport. As a temporary power, we'll take "mimic ability", and use the 1 mimic point for a 6 shift rapport skill.
If you want to do this more often, just purchase the mimic ability power and call it "magical abilities". Treat the skills you use that way as magically enhanced, so they might not work all the time and may be prone to compels or working in weird ways.