Depends. If you retweet something with a hashtag, anyone who goes to that hashtag will see it.
So if #HillarysStools is trending and you retweet or if you send your own Tweet with that # then others can see it unless you have set your privacy settings so only followers can see your Tweet.
think it would be easiest to have a set of hashtags done and saved in notes to copy and paste rather than rekey each time. Yes, I look for shortcuts