The Oxford English Dictionary (OED) indicates that the origin of the word "penguin" is obscure, so at the outset, we need to question your source that suggested a Welsh origin. The OED notes further that "It appears that the name was first given to the Great Auk or Gare-fowl of the seas of Newfoundland." I see that a quick internet search suggests the word comes from the Welsh, Breton or Cornish terms manifesting in Welsh as "pen gwyn ‘white head’, but that is speculative. It would make a certain amount of sense, but it is hardly persuasive and the links between the Welsh/Cornish/Breton and the term of English is wanting. There are also indications of a possible Latin root, but that is also not persuasive.

The Cornish and Bretons were noted sailors, so it is not inconceivable that they would give the word to the Great Auk, which was subsequently transferred to the penguin, but I'd find the explanation more likely if the Auk didn't have a black head (aside from a white spot).