No. Total NO.
If your guys do not clean, carve out, flush out, whatever the AI from the system is, it does not matter what means they use to control parts of previous system - they may use typewriters, ride around on stone bikes, whatever, all of that does not matter as long as they do not understand the system and clean the parts where the AI may be.
Okay, they use perforated paper to program a sequence on a steam pressure cooker - what has that to do with the AI inside of it and it using WiFi as an integrated part of the AI version of an IOT, where it stores its hidden backups - nothing, it has nothing. Yeah it may be sloooow there(or may be not), but it does not mean it can't strike.
Okay, pressure cooker maybe a far stretched - universal matter synthesiser, how much brain it can have - it's probably a complex machine, and what if it controls the only source of food onboard. Navigation, engines, reactor, electricity smart routing boxes, load distribution system, life support, etc. Maybe the AI has a distributed system of its own, in every preasure cooker there is a little bit of it - even though there is no information about that in the question.
A space ship it is a system of connected complex machines and it has to work in particular way, coherent, at proper speeds and feeds, you just can't shove random equipment with different specs and expect for everything work fine. In cases of it making some real work and not just acting as an interface.
Replacing peripheral interface does nothing, replacing core equipment breaks coherence of the system, making a big question - can it still work or not, and most likely not, how fast it breaks, will it blow up (not a trivial question, very important for a rocket, I guess for a space ship also a legitimate concern).
There is a similar/different/less significant compatibility problem - its name is "porting software between Windows Linux MacOS" - you guessed it, it is pain in the rear for anything more complex than some applet, with all the experience and libraries for cross compiling - it still does not always work the same.
And here you throw guys into a system they do not know and wish to replace stuff randomly and rewrite stuff from scratch - it requires a lot of time and a lot of human resources and is not necessarily possible, and you will need to make equipment/hardware from scratch as well, at least interfaces (which are not necessarily helpful, as I said earlier) and not always possible - why is way beyond the scope of the question.
What they have to do is to understand the system, classify, identify components, especially AI related ones. If the AI is in every pressure cooker and they can't erase, reset or rebuild components - then they're out of luck.
If the AI is in some datacores, data center, or on neural chips - reset it, place it in a chroot virtual environment, make safequard around the AI, different monitors etc - then harden your security, harden yourself against rebellion.
It not necessarily a 100% success, as you really need to go through all leaks of intel (and if you can't...)
And there are options after options, scenarios after scenarios, variations after variations on how the situation can develop - the question does not provide enough information about situation and system and all that.
Maybe, they chip out AI datacore and most of other devices are operated by text commands, perhaps some JSON APIs, because founding fathers did foresee the necessity of monitoring and be able read stuff there (real situation), be able to overwrite stuff from a calculator. Etc etc. And the AI even being evil, kept it that way to remove suspicion and whatever other reason (there can be a list of those, valid ones).
Guys have to understand what they do - and use proper solution
Young people may not know, but old - already do backups
Factory reset is a thing even today. You can factory reset AI you can control (there are ways to do it right; just use dumber AIs, more of them etc)
It is possible to clean AI if you understand the system used, at least in principle. AI can't emerge sporadically, we see that in efforts of today to make an AI work. So the threshold for super evil, super smart AI is way higher than tech level you propose, and exceeds our current level. There are limits, there are conditions - it is not magic.
Absence of AI does not mean everything is good - viruses of today show that, so whatever hardware is left can be problematic. Some desync of actions may lead to problems naturally. Best one can do is to monitor for everything you can to detect abnormalities and be prepared to deal with the problems, fix them etc - detecting and understanding and cleaning system bit by bit.
In your question there is not enough information - it is possible to create situation and set resources available when your solution may be the only one, but it requires a lot more work on your side.
Most likely tech is tech of previous generation, or if most of it is lost then highest one they can get, chips from 80's, 90s, 00s, 10s, 20s ... 30s(?) - because the more you leave to be handled with already present components, which you didn't made, more there is places for potential problems, for the AI black box situation as it is present in the question. By lowering your tech for tapes (and really it not necessarily easier than other solutions, Saturn rocket engines are example - we can't make them today, but things are more interesting now) more you leave to be processed elsewhere, more things are out of your control.
Perfect situation is the same tech level, with factory reset equipment, or any hacked T100 options - make your own evil AI, which is evil against that original evil AI - if it can go wrong, make it go wrong in a right way. (But learn your lessons really, there are safe ways to do AI!)
It not possible to omit alternative solutions, because how superficial the question is, it brings irresistible urge to bring some improvements for situation, everyone tries in a way they can.
If you like that steampunk stuff (how it is called whatever) just do it, there is no reason for it, but just do. (Do not expect me to read/whatever however, even if you pay, but it does not mean there aren't people with the same vibe) AI's and movies most books they so lost, even if there are good approaches, nobody uses them. The 'Evil AI' trope is beyond repair.