If the lack of electricity simply means that we cannot get current to go through wires or do not have access to cathode ray tubes, some important things need to change in a rocket: the Computer and the Controls.
There is such a thing as a mechanical computer. Ideally, this type of computer would undergo the shrinking process which electrical computers have. Astronauts relying on mechanical computers may need to carry lookup tables with many needed calculations already figured out. Mechanical computers were actually the computational device of choice for a long time, until vacuum tubes became more readily available.
You could also get lucky and develop biological circuits, but that could be quite difficult to develop. In fact, us real-world humans are only toying with the idea. Loosing electricity may give us the impetus to develop these.
Such a rocket ship would need mechanical controls. Gears and springs would still work in low-gravity, but are quite heavy. Extreme metallurgy, ceramics, or plastics would be needed to make such a craft functional. It is, at least, theoretically possible have a rocket use purely mechanical processes to guide itself.
Some chemical reactions do not really fall under the purview of "electronics." While it is true that electrolysis of water is the process of choice to yield the favorite liquid fuel ($H_2$ and $O_2$) for many rocketeers, you could use plenty of other fuels. There is a short list here of various fuels you can use, and you need not use electrolysis to obtain all of them.
While you do need a spark to get the fuel going, you can always use steel against magnesium like many fire starters do. It would be a simple thing to do so, and can be relatively lightweight.
Given that you can work around your computational and control problems without electricity, most of the other things which go on a rocket do not need electricity to function. Things such as the heat shield, windows, and so on can be made without electricity, albeit in much more difficult ways.
Nota Bene: Electricity simply "not working" does many, many terrible things. For instance, the action potential our nerves use falls under "electricity working." This means all animals would have the reaction time of plants, which are known for not reacting to stimuli quickly. I would suggest re-thinking how much "electricity" you wish your world to have. Taking a hard look at what type of story you want to tell or your audience is critical here.