I got a bunch of answers from the linguist corner:
"The correct pronunciation in Modern Danish (slightly different from how it was pronounced when he lived) is ['luðˀ.vi 'skødə] in approximated IPA. This is not exactly easy to pronounce for an English-speaking musician, though. I’d probably pronounce it like ['skʊdə] (with the [ʊ] being like the u in ‘put’) if saying it in English, I think."
and
"also known as Ludwig Skutte (with an umlaut u), " ... and apparently in the old ABRSM book he was listed to rhyme with "shooter" or like the German "Schuette" (u with Umlaut).
KP
"