"exact file signature this fix is good"
For the PS1 this gets tricky. There were a thousand different file formats back then and everybody used their own preference (various companies would do the nudge nudge, wink wink "we are "accurate" when it comes to ripping" thing for PS1 games). What survives to this day, and what a given ROM hacker would have opted to use is anybody's guess. Ideally they would have made it for the "Scene" (there was not much of a Scene as it was known in older devices and devices since but there was something at least) and a modern best practices method.
Sadly it is not necessarily like some other systems where it is often just a simple header tweak (or missing dumper header), or someone decided to infill a junk section with a different type of random data, such that you can often just tell xdelta to ignore the input hash and carry on with life. You can try if you want.
Xdelta does also have a couple of versions, which can be mutually incompatible, and the GUI programs don't play nice. Said versions as far as ROM hackers are concerned are usually the older version (made before it got an official Windows port https://www.evanjones.ca/software/xdelta-win32.html
, and the more modern stuff from http://xdelta.org/
, which might also have a couple of choices depending upon version numbers).
The resulting thing. Looks like a bin-cue setup. A fairly standard iso storage/burning/mounting... solution. Not my personal preference if I can help it (if I am going to have useless files then I might as well just have a single one) but a perfectly acceptable one used by loads of people.
I never actually made any PS1 conversions for the PSP so I am not familiar with the tools. Assuming it just wants an iso though then there are any number of tools out there which convert between said thousands of formats (while IMGBurn will burn them all day long I don't know if its ISO handling side will take that and spit out a plain ISO, most of the other choices I know of are paid software -- things like ultraiso, magic iso, DiscJuggler...). Alternatively if it will burn a directory or take it from what it thinks is a CD drive then there should be plenty of things that will mount said bin-cue setup and you can present it accordingly.