Whilst I am doubtful the 'in-built' pre amp is going to provide Super Hi end audiophile quality, I am thinking as others have suggested, utilizing it, may be a better option. Although, that said, it seems the Original cartridge (as fitted), to this Denon was the
Denon 9410037907 see here:
https://denon.encompass.com/item/12429230/Denon/00D9410037907/ which may actually have been manufactured by Audio Technica and has similar specs to the AT91.
Also, I think the issue may be as suggested previously, an incorrect Capacitance or Load issue.
From what I can ascertain, the Original Cartridge wanted to see a load capacitance of 100-200 pF and a load impedance of 47,000 ohms.
The suggested AT95 series has Identical Load requirements to the Original Cartridge.
Shure’s recommended capacitive load for the M91E and M91ED is in the range of 400-500 pF !! I'm not sure about it's desired impedence but is probably similar.
It's probably safe to assume the 'in-built' pre amp is providing an input for the Original cartridge that is ideally suited and happy with, whereas Not so with the Shure.
Difficult to say What Load variance would be seen when switching the in-built EQ module Off AND what loads Your amplifiers Phono Input would be providing.
BTW, I'm 68 and I used to sell the Shure M91, Way back when I used to sell HiFi in my late teens and early 20's !! and whilst acceptable, it was not that spectacular, or note worthy lol there were Many better cartridges.
It may be best (as others have suggested) to 'Ditch' the Shure and get an Audio Technica that will be Happy 'Seeing' the in-built pre amp
You'll probably get Good Money for the Shure on Ebay
What Amp are you using ??