We establish new results on the I-approximation property for the Banach operator ideal I = Kup of the unconditionally p-compact operators in the case of 1 ≤ p < 2. As a consequence of our results, we provide a negative answer for the case p = 1 of a problem posed by J.M. Kim (2017). Namely, the Ku1-approximation property implies neither the SK1-approximation property nor the (classical) approximation property; and the SK1-approximation property implies neither the Ku1-approximation property nor the approximation property. Here SKp denotes the p-compact operators of Sinha and Karn for p ≥ 1. We also show for all 2 < p, q < ∞ that there is a closed subspace X ⊂ ℓ q that fails the SKr-approximation property for all r ≥ p.