Want a new mild razor

the Henson DE is a mild and efficient shaver for cheap.

Don't put your eggs into the Asylum 17-4 basket, unless you have some sort of "in" with Phil. As far as I know, he's only doing a limited run of like 100 of them; the first pre-order (25?) sold out in minutes, and if you're not on Bullgoose at the right time, you won't be getting it.

Pre-order was for 50 razors per Phil yesterday. He is also planning a run in titanium that is in the works next.

the Henson DE is a mild and efficient shaver for cheap.

+1...

I solely use this razor now. I liked it so much, I bought the Titanium. As Andrew said it's mild and efficient. The way the razor head is built, it's also intuitive, naturally guiding you to the proper angle.

I too recommend the Henson, in either mild or medium aggression.  I use both the Henson AL13 Aluminum with medium head and the Henson Titanium with aggressive head.  IMHO, there are equal razors in shave quality, but none that I have found that shave better with no irritation (with Astra and other mainstream blades).  Both are a great value for their respective materials.

Fatip Piccolo

Feather AS D2 . Very mild, very expensive.

the Henson DE is a mild and efficient shaver for cheap.

Yeah, this is what I was going to recommend as well

Don't buy anything expensive.  I would suggest a Gillette Tech pre-war(triangle shaped slots on the base plate).  Not only is it mild, it is fairly cheap, will last forever, and will give you great shaves.

The all brass pre-war Tech is the perfect razor for everyone, you can spend more money on a razor but it won't buy you a better shave.  

The Christopher Bradley Karve razor (brass) was modeled after the Tech, according to the owner.  After getting one in 2018, I liked it so much I sold all other razors except the Tech and my Gillette Slim. But as bkatbamna says, a Tech, specifically the pre-War triangle slot, is a great razor and often found on "electric"-Bay. Mild, yet easy to get a great shave, even if you have to take more strokes than an aggressive razor. It is my travel razor.
This is the one I got off eBay (listing photo)

And this is after warm soapy water and a soft tooth brush, followed by a light Flitz polishing treatment

Perfect! 

I have no experience with the Seygus. The Asylum 17-4 has a lot of promise, but as far as I know very few have used the prototype, possibly only Phil.

Others to consider, depending on your preferences:
H&S N075 Mixed Metal
Tatara Masamune (possibly with Nodachi top cap, again it depends on your preferences)
Henson Shaving
Yates Precision M
Game Changer 0.84

(The Yates and the Game Changer 0.84 may be considered by some to be more on the "Medium" aggressive side than "Mild")

There are many others, but these are ones that I've used and would recommend.

I'm sure others can comment on razors such as the Lupo 0.72 and the Game Changer 0.68.

I agree with the suggestions above.  jbreakfield's list here is a good one.  I would add that you might really want to consider trying a razor.  Some of the quality artisans, and in this list, that's at least H&S and Yates, stand behind their products by allowing returns, assuming, of course, that you take care of them during the return period. It's 30 days in H&S's case and 60 days with Yates.  So you can try them out.  Razors seem incredibly individualized so being able to return is really a great option, particularly since these periods are long enough to allow several straight days of shaves with the razor and give you a chance to really see if it works for you (and most likely try them with differing blades, since blades effectively alone seem to vary greatly from razor to razor, at least in my experience).    Otherwise, of course, you might be disappointed: for instance, I tried the Henson AL in the DFS passaround here and I didn't particularly like it -- it really wasn't aggressive enough for me and I didn't find it as smooth as my H&S N075, for instance.  It would not be a razor I'd reach for with several days of growth, that's for sure.  So a thought to consider:  try the razors you can return.