Yes, just avoiding any copywrite infringement issues by renaming characters, locations, items etc, and not using any recognisable art assets like logos, emblems etc.
If you intend to make your game playable to the public, even for free, then this is a must as Nintendo will otherwise shut you down. If you only intend to release screenshots and footage you might be able to fly under the radar, but Nintendo would still be within their rights to take down your videos from Youtube and stuff.
Best policy is to play it safe and make it unaffiliated with Zelda, but still capturing the spirit and style of the original games.
Good luck, and have fun 
learning from scratch can be overwhelming at first, but it gets easier over time.