I have a small sharps bin which lives in my testing bag.
As an T2 who tests every now and then it isn't a big issue, because I test mainly at home, but I do have a fall back option of an empty test strip tub which can act as a short term sharps bin.
As far as I know in the UK you are supposed to put all used sharps in a sharps bin (and anything else contaminated as well). I don't change my lancet very often, but when I do that goes into the sharps bin. Each test strip goes in, along with the patch of kitchen roll used to mop up the gushing blood from my wounded finger.
Realistically I don't constitute a threat to anyone clearing out the bins, but the rules should apply to all because HIV and hepatitis can be transferred by used needles and nobody can tell where the used sharps came from once they have been "binned".
The rules are usually there for a reason.