They're both fine. In such contexts, any is usually just an optional "intensifier" - which can be further emphasized by giving the word extra stress...
1: Will you please stop asking to borrow a few pounds? I already told you, I don't have any money!
But there can be another significant difference in meaning. Consider...
2: I don't have alcohol in my house
3: I don't have any alcohol in my house
4: I have no alcohol in my house
As a native speaker, I'd normally understand #2 as implying I don't allow alcohol in my house (so don't try to bring any in), but I wouldn't normally distinguish between #3 and #4. Mostly, they'd probably just mean If we want to continue drinking at my house, we'd better buy some alcohol to take back, because I haven't got any.
It's just possible I might prefer #4 (without with intensifying any) if I knew I had some long-ignored sickly liqueur at the back of the drinks cabinet. But probably not - native speakers aren't usually that precise about how we express the negative in such contexts.