The smart people all may be busy so, I thought I would throw some thoughts at you.
Without knowing what the vertical scale setting was on your O’scope, the majority of that noise may just be power supply or other noise from active components. If the unit is older than 10-15 years, all electrolytic capacitors may be drying up and getting noisy. If it has opamps, I would try replacing those. More modern ones like Burr Browns are much quieter. Is the noise noticeable like bacon frying? That would be a good clue.