I have done some research and found out that "won't " suits the sentence better. Having said that, the grammar form 'so that + infinitive ' can be used in many ways with various tenses and, with respect to the sentence in question, won't (will not) suits it well.
I was referring many dictionaries, but couldn't find a satisfactory definition, but the website speakspeak.com explains the very mentioned grammar form beautifully. I've taken the references from there and it goes as follows:
So that vs. to + infinitive: expressing purpose
We can use so that + can / could / will be able to / would have to say that one action makes another action possible:
1.I’ve bought a dictionary so that I can learn more.
2.I bought a dictionary so that I could learn more.
3.I’m going to buy a dictionary so that I can (or will be able to) learn more.
4.We arrived at the theatre early so that we would have time to eat before the show.
Look at the third example mentioned above.
We use so that + don’t have to / won’t have to / wouldn’t have to to say that one action will help us avoid having to do something else:
1.I’m going shopping this evening so that I don’t / won’t have to go tomorrow.
We use so that + won’t / wouldn’t / don’t to say that one action will prevent another thing happening.
1.I’ve brought an umbrella so that I don’t / won’t get wet.
2.I’m going to bring an umbrella so That I don’t / won’t get wet.
3.I took an umbrella so that I wouldn’t / didn't get wet.
4.I always carry an umbrella so that I don’t get wet.
Here, look at the second example mentioned.
We can see that future happening always go with "will"
And activities happened in past always go with "would".
The sentence could be modified as , "We're going to pack all the books in wooden boxes so that they won't get damaged."
Thanks. Hope it all helps.
Best Answer
Ditto @matias, but let me add that the more common situation is that "would" indicates intention and "could" indicates ability. If you said, "I asked Bob for help but he couldn't help me", you are saying that Bob was unable to help you. Maybe he wanted to help you, maybe not, but it doesn't matter because he was not able. If you said, "I asked Bob for help but he wouldn't help me", you are saying that he was able to help but he refused.