There is something also awry with the sequence of battalions you cite.
16 Battalion Welsh Regiment was disbanded in February 1918 with men going to 19th and 5th Battalions Welsh Regiment and to the Corps Pool.
13 Battalion Yorkshire Regiment reduced to cadre strength in May 1918 and in July 1918 absorbed 19 Battalion Yorkshire Regiment.
1/4th Yorkshire Regiment didn't absorb any other battalion.
While an individual movement between the Welsh and Yorkshire Regiments was entirely possible (see the London man Charles Albert) it would not have been as a result of regimental re-organisations.
Fold3 on Ancestry has a pension card for (mis spelled) Aron Charles Wilson of Bargoed born 1896 discharged 21 Mar 1919 service number 21489 in 3rd Welsh. This links with a medal card for 21489 Charles Wilson , National Archives here:
https://discovery.nationalarchives.gov.uk/details/r/D5930122, the medal roll says he went to France with 13th Battalion Welsh Regiment and served throughout with that battalion.
My feeling is that the unsuspecting Charles A Wilson of London's number and possible service has been seized upon as belong to the Bargoed man.
MaxD