It depends.

For wallets using hardened keys, it is fully safe to export private keys with zero risk of the whole chain of addresses getting compromised if a single key gets compromised.

However, if your wallet happens to create unhardened keys. Given a public parent key and a private child key, you can calculate the private keys of the entire chain of addresses. This is very dangerous if you do leak the public parent key.

I'm not too sure about Armory however.