My understanding is that there are also single edged razors that don't work with double edged blades, but they are way less popular. /r/wicked_edge has a guide here [0] basically, buy a Vintage Gillette Super Speed Razor on ebay (or really anything you want, handles can't be that different, they're just 3 pieces of metal) and a pack of sample blades on tryablade.com
[0] https://www.reddit.com/r/wicked_edge/wiki/de_kit
https://www.reddit.com/r/wicked_edge/comments/4exeep/beginne...
I've always found the reviews for Trumper soap incomprehensible as it never lathered and if by miracle some lather was produced, it would not stay longer than half a minute...
Here's some for window scraping: https://www.amazon.co.uk/BOHLE-Spare-Blades-Laminated-Scrape...
Here's some that claim to be single edge and for shaving: https://www.amazon.co.uk/Gem-Personna-single-stainless-blade...
Basically the old razor blades that appear in movies when people have to cut themselves :)
The biggest difference from modern razor blades, other than taking up much less space, is that they are manufactured by different companies and so there is real competition, which makes them massively cheaper.
That said I still haven't been able to get near as good a shave with them as I do with the Gillette power thing that I have, which annoys me.
My current razor (seldomly used as I'm bearded now) is a Weber DLC coated DE razor. It works nicely and doesn't get gummed up with cut hair.
My understanding is that different blades suit different complexions. For example, the platinum blades I've tried are too sharp and irritated.
Get a sampler with a few dozen blades for $10-$15. Then get the blade you like for $20 for 100 blades.
I'm very satisfied. Not coming apart is a significant feature. The case is nice too; I've used it several times to look at the back of my head.
I haven't found any blades that don't work. As far as I know they're all the same.