How to keep cat urine sample fresh ?? Should I stick it in the fridge?

Yes. you can refrigerate the sample until just before you head to the vet to drop it off. Just let them know that when you collected it and that you had it refrigerated. A sample that cannot be analyzed right away should be refrigerated and can be for up to 24 hours. If it sit unrefrigerated for more than an hour then I would suggest collecting a new sample and refrigerate it right away.

try getting one before you have too go

If it is for crystals, then it needs to be a very fresh sample like within an hour. I think regardless, you should get a fresher sample

recollect seems more hygenic

When my cat seems to have difficulty to weak or interrupted urine flow,
I spread a small cutted Saran Wrap over in the toilet. Even the quantity
is not much, I try to tie a rubber band around the sheet in order to bring
it to a vet for examination.
I always keeps it into a glass bottle and store it in a refregirator until
I go and see a vet with my cat.

Fresh for what are you going to drink it ?