Both JSB and H&N make "lighter" weight alloy pellets, of the hollow base, round nosed 'waisted'(diabolo) design.

I have never seen this lube, prior to this thread.

Once must be careful with lubes in springer (spring compression) air rifles due to the high heat generated when the air is compressed. Ignition of the oil is a definite possibility.
This is hard on the seal as well as fouling the "then" combustion (compression) chamber.

Both JSB and H&N make "some" of their pellets in multiple diameters of basic .177 and .22calibers, listed on the boxes.

I do not know if they do this with their .25 cal. pellets.

I see 6.3mm is .248". I do not know if THEY make this size, but .250" pellets should easily be sized down.