Not exactly non-offensive. Calling a Welshman Taffy in a crowded Cardiff pub is very likely to earn you a punch on the nose.
As with Jock for Scottish or Mick for Irish its use these days would generally be frowned upon.
Immortalised however in the famous piece of doggerel which exists in a variety of versions, commemorating the Welsh cross border raids of centuries past;
Taffy was a welshman, Taffy was a thief
Taffy came to my house and stole a piece of beef
I went to Taffy's house, Taffy was not at home
Taffy came to my house and stole a marrowbone
I went to Taffy's house, Taffy wasn't in
Taffy came to my house and stole a silver pin
I went to Taffy's house, Taffy was in bed
I took up a poker and flung it at his head