Chalk is your best bet. Rip has a callous video, and I've seen others, which might address your concerns (I haven't watched the whole video of Rip's).
You're going to need some callouses because your next option is most likely going to be blisters if you whittle those things down too much.
Was your girlfriend really complaining about them, or just drawing attention to the fact that you have them? I couldn't imagine many women really wanting you to have hands just like theirs. She might just be shocked by them, but she'll probably adjust.