You need to be more specific about what you want, perhaps provide an example of the kind of things you would like to do.
I would say biomedical engineering would be a good one but you have ruled out engineering.
The main thing left in my mind is degrees that equip you for a technician type role. You can also aim for a technician job later on (sleep technician, cardiac technician, etc). Some courses teach you about biomedical instrumentation and measurements (i know BBiomed at Swinburne does, other uni's may as well). You can probably find a course that contains a lot of that type stuff. This would chiefly include taking biomedical measurements of patients using technological tools (blood pressure, ECG, sleep lab stuff, etc).
If you mean more computers, things like Health Information Science and stuff like that would be a good bet, alongside things like data science where it's applied to medicine.
Psychology and physiology at the later year stages may allow you to undertake projects where you can use MRI data (and during honours, potentially MRI data gathered exclusively for you/with your help).