Before revision:  The scaling of the swimmer velocity V with the force amplitude A is analyzed in details and this shows that at small enough A, V\sim A^2/\eta^2, whereas at large enough A, V is independent of the force and is only fixed by the stroke cycle frequency and the swimmer size.
After revision:  The scaling of the swimmer velocity V with the force amplitude A is analyzed in details and this shows that at small enough A, V\sim A^2/\eta^2, whereas at large enough A, V is independent of the force and is determined solely by the stroke cycle frequency and the swimmer size.