Having a single URL for each page is known as URL Canonicalization. Canonicalizing the URL for each page has been an SEO best practice for ten years or more. The search engines won't think badly of you for redirecting your short URLs to your long URLs, doing so may even improve your rankings.
This StackExchange site implements redirects for canonicalization. There are short sharing URL. (Click the "share" links and see for yourself.) These short URLs and incorrect URLS all redirect to the correct full URL for this question:
You can implement URL canonicalization with either 301 permanent redirects, or by using link rel canonical tags in the head section of your pages. See the Google help document on using canonical URLs for more information.