The chip might be programmable, but it might be a purpose designed/built chip whose datasheets were only ever kept on paper and are buried under hundreds of feet of landfill rubbish now.
I would focus on electrolytics and not worry about the film caps unless there is a good reason to do it. The film caps might be part of an analog circuit that you do not want to risk de-tuning. Many but not all electrolytics in this kind of circuit are for power supply purposes, so you don't have to be too careful about value or tolerance. For instance, you can replace a 220uF electrolytic with a 330uF cap if you are in a pinch in those cases. If you are talking about an analog accumulator or filter though, you want your capacitor values to be spot on.
Tantalums were brought up earlier in this thread. They are far superior to electrolytics on most fronts, but there are some trade-offs. Tants hate reverse voltage and will smoke if stressed in that manner. If you run them close to their rated voltage for years on end, they tend to fail either open or shorted. As an example, some of the old Tektronix spectrum analyzers have a component that has a 16V tantalum on a -15V rail (or somewhere thereabouts, just going from memory). Over time, that capacitor fails, and you end up losing one of your oscillators, and in my case, the entire rail was shorted out which put some stress on the power supply and took out anything else needing that -15V rail. One of the preventative maintenance actions for such equipment is to remove that capacitor before it goes bad and replace it with a tantalum with a 25V rating. You are on the right track with picking automotive grade and 125°C temperature rating.
Is this module doing what I read earlier in the thread about holding the speed when the button is pressed? Knowing things like this provide great clues when taking the cover off a black box.