I am using a west coast razor with astr blades currently. I have sensitive skin but have not had any issues since I made sure I was shaving wtg on the first pass, particularly on my neck.
I use Personna Red blades, Parker Variant razor with Arko as my usual shave with an Omega synthetic brush.
Face lathering and two passes (4 & 2 on the variant) gets a DFS to near BBS shave with no irritation at all for my face. I would characterize my skin as being sensitive. I will also use Captain's Choice 45th parallel shave soap depending upon my mood, it's a great soap and fragrance.
I have sensitive skin. I use a few different razors and blades. Razors/blades: Gillette Slim Adjustable, I set at 6 and use either a Gillette 7 o'clock Permasharp(India, tied for my favorite) or with a Wilkinson Sword Classic(other favorite). Gillette Super Speed(mild razor) with a Feather blade(works great in this razor) or either of my 2 favorites also work. Gillette 3 piece Tech, another mild razor and it works great with a Feather. Merkur 34c I haven't used in a while but works with the 3 blades I like. Wilkinson Sword Classic(mild razor) with a blade of the same name, I can get a nice irritation free shave with this razor but just not all that close. Schick Krona, haven't used it enough to find which blade works best in it. Last I have a Schick J1 Injector(my Dad's), it is quite aggressive and I only use it on occasion for that reason.
Ive got a few: an '80 Gillette Super Speed and a Timor 1351, both of which I use with Timor blades. My daily shaver is a Harry's Winston though.
Im a ginger, so my skill is kind of sensitive and all of those razors are great shavers which dont really cut me. Everyone's skin is different though and what works for me may not work for others.
I like Feather blades in my Gillette Superspeed and RazoRock Wunderbar. I don't think I have sensitive skin, but I still need to be careful about angle and pressure if I want to avoid irritation.
Razor: Merkur Futur
Blades: Wilkinson sword (want me to send you a sample?)
I used to have very sensitive skin until I switched to straight razor.
Now I have no skin.
I've finally settled on a Rockwell 6c with either the 4 or 5 base plate (depending on how much growth I have) with either a Feather blade or a Gillette Nacet. The feathers are sharp, but I'm really liking the Nacets. Almost as sharp but even smoother than the feathers. I have super sensitive skin with a super coarse and thick beard. Pretty crappy combo, but with the Rockwell and a somewhat aggressive base plate with a sharp blade I can make it work if I use a light touch.
I use a DE89 with Feather, KAI, and GSB (depending on mood).
My face was sensitive when starting out, but now 18 mos in either it go better acclimated or I got better technique!
After experimenting with blades, I'm now going to try different more aggressive razors starting with a Maggard V2 OC. I also have a Maggard V3A SB and Schone OC to progress to.
My skin is average in sensitivity. Currently using a '38 Sheraton razor, and Rainbow blades. Another favorite razor is a '46 Aristocrat, which is milder.
I am more sensitive to soaps and cream and using a bad blade for me just amps it up even more. If you believe you have a soap with good glide/performance then try other blades. Everyone skin is different when it comes to blades. Example: Voskhod blades are quite popular but they just scraped the crap out of my face. My suggestion would be is to get a blade sampler pack.
Blade suggestions from me would be:
Wilkinson Sword Classic(German blade)
Gillette 7 o'clock Permasharp(India)
Feather, these work for me in mild razors.