Technology progressed considerably by the time the space shuttle came into service.
The HP41C flew on nine shuttle missions. It was used to perform calculations necessary on the missions. It also served as a backup for the main computer. I had an HP41CV at the time. The difference was that it had four ports that accepted chips, there were ones for math and engineering for example. You could also plug in a card reader for loading and saving programs. It was quite a sophisticated computer.
HP-41C - Wikipedia
It's interesting to note that the Apollo systems started being designed in 1961 and continued to 1965. So some of the technology of 1969 dated back a number of years. That's usually the case with all these type of systems.