Please forgive the unseemly self promotion, but Chain-L is adequate for the ball bearings, and will work well on the internals where the tacking agent will lengthen the service interval. You can also mix it with a high temp auto spindle grease to make a light lube balancing the benefits of oil and grease (I'd estimate 10-20% grease blended into the oil).

Or if you want to stay with grease on the balls, you can do so, then oil by backing off the left cone enough to run oil down the axle and past the bearing. Slight thinning, or even replacing grease won't hurt since the left bearing operates at about 1/3 load of the right.

BTW- I'm not selling anything, since the OP already has the oil.

If you really want to make an oil port, the easier way might be to make a through the axle oil port. Start with a long QR axle, long enough to use as a nutted axle. Gauge a spot along the axle where you'd want the oil to come out. Cross drill a 1/16" or so hole through one side. Finish by jamming a piece of wooden dowel, or other filler to block one end of the axle up to the hole.

Oil, by turning the wheel (bike) on it's side, drip some oil into the axle, and it'll drain out the side hole into the hub. Finish by capping or plugging the working end so the inside stays clean until next time.

If you can't use a hollow axle, or can't drill one, you can file a groove or flat on the left side leaving a gap you can slowly drip oil through, past the cone and into the hub. This will be a slow process, and it'll be harder to close, but can be made workable with some creativity.