Rderry
I had a look just now on my CD (alphabetical) of Boer War Cavalry and there is one "4586 Pte. R.Jones" listed for the 19th H (initials on supplementary roll as "R.H."). There were a few under "Phillips A" as you might expect - but none with the 19th H. It is necessary to point out a few caveats here; I am relying on correct spelling of surnames (and sequence of initials) and also your nominating the possible unit. Frequently, questions relating to family history are asked on this forum - and often there is just no possibility of providing an answer.
Your rendering of the sword markings looks a bit odd. Exactly which part of the sword are the markings you describe? On the blade near the guard or on the hilt? What is the length of the sword blade? A photograph of the markings would assist greatly.
In any case, it would be most difficult to definitely state that a particular sword or weapon was actually issued to an individual. Unless it was marked in some way or tagged.
Good luck with your quest.
Regards
IL.