Old English had multiple dialects. By convention, words are usually cited in the West Saxon dialect, I think because this served in some time periods as a kind of widespread standard. I think "/wiːt͡ʃ/" is just the form expected according to the rules about how pronunciation usually developed in this standard: it seems plausible to me that other pronunciations such as /wɪk/ or /wik/ may have existed.
The consonants [k] and [tʃ] were originally not distinct, so they can show variability between different Old English dialects
The sounds [k] and [tʃ] are particularly complicated. They were spelled in Old English with the same letter, C, because they developed from sounds that were not originally distinct. Some scholars argue that even throughout the Old English period, the sounds were not actually distinct in the same way that they are in modern English. [tʃ] comes from /k/ in contexts where it underwent a process of "palatalization". But different dialects appear to have had palatalization in somewhat different contexts.
Furthermore, there is speculation that in some dialects, or in some periods perhaps in all dialects of Old English, the palatalized pronunciation of the letter C had not developed as far as an affricate [tʃ], but was instead a plosive that could be transcribed in IPA as something like [kʲ] or [c]. There is no simple way to describe this sound in terms of modern English sounds, but the "ky" sound at the start of "cute" might serve as a rough approximation. In the context of dialect mixing, a speaker of a dialect that used [tʃ] instead of [kʲ] or [c] might hear the palatalized but non-affricated [kʲ] or [c], and perceive it as a non-palatalized [k] sound.
The Wikipedia article "Phonological history of Old English" says that as a general rule, a C at the end of a word became palatalized after the vowel I in the West Saxon dialect. But dialect mixing could easily lead to exceptions to that rule, and we have evidence that such mixing did occur in some way.
The vowel i in Old English usually is long or short according to the etymological origins of a word
With the vowel in -wic, the situation is a bit different. Old English spelling didn't distinguish long and short i as a rule (writing ī is a modern convention for the convenience of modern readers). But as far as I know, there was not much notable variation in pronunciation between long and short i in different dialects of Old English, and we can look at etymologically related words in other Germanic languages to get a good idea of whether an Old English i was originally long or short.
The Oxford English dictionary indicates that English wick, n.2 "abode, dwelling, dwelling-place" (traced back to Latin vīcus) is cognate to German Weichbild and Dutch wijk: the vowels ei and ij clearly indicate an originally long i sound in this word.
The OED entry for wick, n.4 "creek, inlet, or small bay" (traced back to Norse vík, from a supposed Germanic base wῑk-) also shows an etymologically long vowel quality.
Wiktionary seems to instead say that these have the same ultimate origin, explaining the bay meaning as "[arising] by association with harbor towns" (Reconstruction:Proto-Germanic/wīkō).
Although the overall etymology seems a bit of a mess to figure out, it does seem reasonably clear to reconstruct the vowel as originally long.
But Old English may have shortened originally long vowels when they came to be in unstressed syllables
However, one thing that Old English is thought to have had in common with modern English is the potential for reducing vowels in syllables with a lesser amount of stress, such as the second elements of compounds (especially for those elements that came to act more like suffixes). See the note at the end of Alex B.'s answer here.
I don't know enough about Old English stress patterns to say whether that could have applied in Eoforwic, but if it could, that could explain how an originally long i came to be shortened.