No, no Henrys. The name doesn't seem to have survived in the family anyway. Lots of Johns & Roberts though.
The only concrete info I have is from Arthur's marriage certificate, and that is only a transcription. I have not managed to see the real thing. Arthur was born roughly 1832 So I am assuming his father would have been born between 1800 & 1810. But I know there were a ton of Shaws in County Down