im not up to spec with the molecular weight of hcg and what kind of filter you would use, but i will come in and say that subcutaneously injected drugs such as this one, although aqueous, do not attract the same risk of negative outcomes in terms of pathogens as anything injected intramuscularly. if i were personally reconstituting something like hcg and injecting into the skin, assuming that i had acquired human grade hcg and water for injection, i would not bother with filtration since i simply see it as unneccessary.
debris/pathogen injected into muscle tissue = highish risk of abscess, and if abscess develops, more complications/wound severity
debris/pathogen injected into skin = much much much lower risk of abscess in the first place, and if one does develop, wound severity is far less ie you would likely get a boil or pustule that would break the skin surface and therefore be repaired by the body easily, rather than a huge area of necrotic tissue as per intramuscular injection, that would bring up all sorts of complications
cheers