For most fb sweepstakes liking a page is a requirement of the sweeps and your liking it will show up in your timeline, but you can just delete the message that shows that you liked it.When you hit share, it will show in your timeline that you entered the sweeps, but you can also delete that.
I have an fb account that I use just for sweeping, so I don't really worry too much about the privacy thing because I don't really have any personal information on there and I have no friends on that account.