“Hydrogen peroxide will lose effectiveness over time from contact with oxygen.”
Flame on!
No, it off gasses slowly in oxygen into any headspace. Â Minimizing the headspace, but more so, minimizing the storage temperature, UV light (that’s why it comes in brown bottles), and any contaminants (iron will instantly catalyze the degradation to H2O and O2.
Pedantic flame off!
Booties: As someone else said, way upthread, source them from musher’s suppliers.  Used to go for a $1 each in quantity from local sewers in my town, probably more now.  A set for $29.95 at REI is heavier (needlessly so) and less comfortable for the dog than the simple one-layer / thin velcro closures.  The mushing ones come color-coded for size so you can get the correct bootie on the correct dog (Iditarod mushers have  64 to put on 16 dogs, plus a hundred or so extra ones).
OMG! Â Looking for images, I find that there are now dog booties for $49, $79 and $89 a set. Â DON’T GET THESE:

Get this style:




This should help keep her from shivering at night.


