indenture records for a Chemist and Druggist are kept in Wales
As far as I am aware there are no apprentice records of the type you seek held on the catalogues of the Pembroke Record Office or the N.L. of W. catalogue.
This would suggest that no such records exist, however you could try National Archives.
There are references in my transcription of the Borough Minutes of children being "put out" to apprenticeship at the cost of the Council (also referenced in my transcription of the Accounts of Council), however there is nothing for the period of your interest.
Rgds
Owen Ap Benfro
