I use various brands of 15W-40 "diesel-spec" oil, i.e. Delo 400. No issues with low oil pressure. The cap registers to the oil pump body with a metal-to-metal fit, and the O-ring is compressed in a defined gap. As long as it is not leaking or so grossly oversize that it distorts the cap and/or prevents the metal-to-metal contact from occurring, there can be no effect on oil pressure.
One of my pumps was leaking, so I simply disassembled it and measured the old, compressed O-ring, as well as the cap.
I've run the Buna-N oil rings from American Seal (Dichtomatik) for several years. Viton material would be a potential upgrade, but I'm convinced from inspecting the Honda original that it must have been Buna.