Matthew Ryan, in his text to accompany his images below states:
"The shaft of the arrow was removed but the bodkin remained, left embedded into his skull to a depth of around six inches. This was later removed at Kenilworth Castle by some ingenious work of the surgeon John Bradmore
who later went on to write a detailed account of the procedure."
www.facebook.com/matthewryanhistoricalillustrator/media_set?set=a.842095342540698.1073741879.100002207204372&type=3
and more of his great art work on his website
matthewryanhistoricalillustrator.com/
You can read more about Henry here
meanderingthroughtime.weebly.com/wars-of-the-roses-blog/king-henry-v