If I understand well the question, you want to exchange the buffer of your 4 kDa protein solution by filtering using a 3 kDa UF membrane. I don´t have experience with this type proteins but according to my experience in UF, the membrane should be able to retain your protein with little or no losses (unless protein hydrolysis occurs).
In MF and UF we frequently face the inverse problem to yours, it means the solute which is supposed to permeate the membrane according to its molecular weight, gets rejected by the membrane due to absortion or complexation with other molecules.
As per my knowledge, one thumb rule for selecting ultrafiltration membrane molecular weight cutoff is that the MWCO of membrane should be 1/3 to 1/6 size of the targeted retentate particles. Otherwise the rejection will be more.