In Go, a string is really just a sequence of bytes, and indexing a string produces bytes. So you could simply split your string into substrings by slicing it into 4kB substrings.

unicode/utf8
package httputil

import "unicode/utf8"

const maxLen = 4096

func SplitHeader(longString string) []string {
    splits := []string{}

    var l, r int
    for l, r = 0, maxLen; r < len(longString); l, r = r, r+maxLen {
        for !utf8.RuneStart(longString[r]) {
            r--
        }
        splits = append(splits, longString[l:r])
    }
    splits = append(splits, longString[l:])
    return splits
}
[]bytestring[]byte