Is there an Old English-derived word for change/alter/modify?

I think 'wend' is a good choice. I have a book on my desk in German and 'wend' is used in this way too: "Magdeburg - Wendezeit und Neu Beginn" (Magdeburg - Changing Times and a New Beginning). It describes the city's shift from the East German system to the West German one in the early 1990s.

wrixlan is cognate with German wechseln and has just that meaning. wordum wrixlan is the poetic phrase meaning to compose poetry by shifting and braiding words together.

Shape derives from Old English; the OED concisely says of its origin, "A word inherited from Germanic." In modern English, it means several things, including changing or modifying something, often for the better. Merriam-Webster, passim:

3. : to adapt in shape so as to fit neatly and closely / a dress shaped to her figure [...]

5a. : to make fit for (a particular use, purpose, etc.) : adapt / shape the questions to fit the answers

b : to determine or direct the course or character of / events that shaped history

c : to modify (behavior) by rewarding changes that tend toward a desired response

Shape is quite versatile and common in English. For example, colloquially, I could say shape up or ship out (Wikitonary), or I could shape policy (LSE).

In Old English, scieppan was a word for creation as well as shaping, such that God was called the Scieppend or the Shaper (Barney, Word-Hoard: An Introduction to Old English Vocabulary, p. 35).