I use liquid dish soap and a toothbrush on new equipment, or used equipment that is really dirty. I've never had a problem with soap leaving residue I could taste. You don't even have to rinse it all that much to remove residue. It's amazing what can come off of even new equipment. Residue from manufacturing, etc. I cringe to think that for years, I used stuff out of the box without even washing drip tips, etc.
When I'm rewicking or recoiling an RDA I've been using, in all honesty, I just run it under hot tap water. Hot water seems to remove any buildup or residue that accumulates between weekly rewicks, etc. Maybe I should be using soap here too. However, I vape mostly unflavored juice, so it's not like I have to scrub away different juice flavors.
When I'm building coils, if it's not a complex wire, I wipe it with 70-90% isopropyl alchhol on a cotton ball. I pull the cotton ball the entire length of wire a few times. Within a minute, the alcohol has evaporated and you're ready to wrap the coil. It's amazing what kind of residue is left behind on the cotton ball when doing this, even when you think the wire is 'clean'.
If it's a pre-wrapped coil I install in a device, I just dry burn it (within reason) and assume that will take care of the worst.
In all honesty, I'm kind of grossed out using premade coil heads these days. After seeing the residue that comes off of wire and newly bought equipment, I don't like the thought of what might be in a premade coil head. That's just me though. I don't use them too often these days anyways. I'm sure I've inhaled much worse over the years.