Use a hex editor. You’ll need to find out the relevant executable format for your operating system, of course – assuming you want to use an operating system… I suppose you could always write your own bootloader and just run the code directly that way, if you want to get all hardcore.
I don’t think you’ll really be experiencing what programmers experienced back then though – for one thing, you won’t be using punch cards, paper tape etc. For another, your context is completely different – you know what computers are like now, so it’ll feel painfully primitive to you… whereas back then, it would have been bleeding edge and exciting just on those grounds.