'Surprisingly they do not IME stink, I have found several mummified mice, and never noticed a stink from that area in the weeks before I found them.'
Hi,
That will actually depend on the size of the rodent concerned. If your 'mice' are House Mouse (Mus musculus), they will do relatively little harm, and because of their small size, cause no little or no noticable odour on decomposition.
The Long-tailed Field Mouse or Wood Mouse, (Apodemus sylvaticus) is somewhat larger, and will cause significantly more damage... it sounds like your shredding has most likely been caused by this species. The very similar, but localised Yellow-necked Field Mouse (A. flavicollis), is a woodland animal, a little larger still, and just as destructive. They will leave a smell for a week or so, depending on the conditions therabouts.
Of course your 'mice' may, God forbid, may not be mice at all, but the Brown Rat (Rattus norvegicus). Someone told me only yesterday, that the Brown rat is so plentiful in the UK now that anyone is never more than ten feet away from such a rat at any time! I do not / prefer not to believe that for a minute... Whatever, anyone who has had the misfortune to endure the putrid stench of a dead rat beneath the floorboards is unlikely to ever forget it. Our family did when I was a child. I am fifty-one years of age now.
Next... (squeek!) your 'mice' may be neither mice, nor rats: the culprit may be the far more exotic Edible Doormouse (Glis glis). Introduced by the Romans, allgedly, and fattened in large jars for food, these cuddly creatures are known to cause problems, mainly in the Midlands areas. They are particularly partial to apples. If, in your loft your trays of Coxes show signs of chewing, and you can't sleep at night for the noise above. Glis may be to blame.
Finally, if after all that, this is any consolation, the infamous Black Rat (Rattus rattus) - of Bubonic Plague fame, is all but extict in the UK now. Consequently that thankfully rare, black-furred, pink footed, pest, is very, very unlikely to be nasal flavour - of the cold winter months...
Season's greetings. (I enjoyed that!)