Siân: Nice try, but you don't catch me that easily. Y Ddraig Goch may well be of the male persuasion. Mochyn is a masculine noun, although the term describes a pig irrespective of gender, although 'baedd' (boar) is masc. and 'hwch' (sow) is fem..
Presumably 'Ddraig' is the generic form, and there are alternate words for the cock dragon & the hen Dragon.
Alternately, someone may have considered the dragon to be a mere legend, and as with inanimate objects, assigned a gender at random.

However, the best solution is to ascribe the expression "Y Ddraig Goch Ddyry Cychwyn" to a description of the Welsh coat of arms, or to the Welsh flag. In which case, 'flag' translates as 'baner' a fem. noun.
"I bob un sydd fyddlon
Gan ei faner ef"

Hwyl Fawr

Nigel