Re: 1957 Evinrude 35 hp. junction box
I have a pair of '58 Bigtwins, which I rigged with solenoids. First and as previously pointed out, the Mercury starter solenoids will fit in you lower cowl pan better, because they are smaller than the OMC units. Also, do not try to use an automotive solenoid - unlike the outboard units, they ground through the base. The outboard starter solenoids are grounded via one of the smaller terminal posts.
You may also have to remove the air silencer (the box on the carb), in order for the solenoid to fit. I did this and used carb grills off of a couple of Johnson 33hp motors, in place of the air silencers. There is a disadvantage in this, however, in that the motor will be quite loud if you do this. The powerhead in the later OMC 28hp and 33hp motors is essentially the same as yours, but those motors had the fiberglass covers, which kill quite a bit of the noise.
I have never tried to mount the Mercury solenoids along with the air silencers, but may do so soon. I'm thinking about selling the Bigtwins, because I am not using them and I've put the silencers back in, to return them to stock configuration. The solenoids are now out, but I'm thinking that it might make sense to try to put them back in. If I get this done in the next week or so, I'll let you know how it worked out.
On the solenoid rectifier boxes that you are referring to, I would say that they aren't the biggest problem. You can still find them on EBay, etc., but where you will run into trouble, is in finding a cable that isn't so dry rotted as to be useless.
Also, you can tell very easily if your motor was originally built as an electric version v. a manual version. If there is a rectangular "socket" with a number of pins in it, on the starboard side of the motor, it is the electric version. If that is not there, it is the manual version.