I think that's a reasonable choice under the constraints you have given (but see below for accent). You might consider using ἰχθυοθηρητήρ rather than ἰχθυβολος. I think the connotations are slightly different - although I don't think I've met either of these words in the wild, but from the formation, the -βολος suggests striking the fish, while the -θηρητήρ suggests hunting for them.
As an aside, the term "Fisher King" has quite Christian connotations for me, but the word for "fisherman" is ἁλιεύς in the NT, and ἄναξ has a distinctly poetic/archaic feel to it.
One further remark: the link given above to the L&S entry for ἰχθυβολος shows two possible accents, a paroxytone ἰχθυβόλος for an active meaning, and a proparoxytone ἰχθύβολος for a passive meaning. This type of distinction is regular for compound nouns of this type. So, if you choose to go with your original version, it should be ἰχθυβόλος ἄναξ.
Ánax is a fine word for "king", though if you want to be super-ancient you can use wánax (ϝάναξ) instead; that's the even older form found in Homer. The first letter is a digamma, representing a sound that disappeared from Attic but survived in other dialects.
Ichthýbolos is specifically about hitting fish with spears or tridents; I'd translate it as "angler" rather than "fisherman". Varro suggests a few other words you can use, but to add another option, how about a participle? The generic verb for "to fish" is ichthyáō, which doesn't imply any particular method. So "[the man who is] fishing" would be ichthyõn with contraction and ichthyáōn without; the contraction is very Attic, while Epic and many other dialects don't do that.
So for a particularly archaic sound, I'd say ὁ ϝάναξ ὁ ιχθυάων ho wánax ho ichthyáōn "the king who is fishing".