This app was mentioned in 4 comments, with an average of 1.75 upvotes
Tripods are always a good idea. Even if you think you're holding the camera completely still there's still some vibration. It's most obvious when the shutter is open for longer periods. You can minimize the effect by bracing your hand against a solid surface (such as a stack of books) but it's still best to use a tripod. It's even better if you can activate the camera remotely so you don't have to touch it to take the shot.
I have the exact same camera. It has built-in WiFi and if you have a smartphone Nikon has an app you can install. It allows you to trigger the shutter remotely and download pictures wirelessly to your device. I have the Android version and it works fine for me on my HTC One M7. You have to be connected to the camera hotspot though. You can't connect it to your home WiFi AFAIK.
https://play.google.com/store/apps/details?id=com.nikon.wu.wmau&hl=en
https://itunes.apple.com/us/app/wireless-mobile-utility/id554157010?mt=8
The WMD app is the official Nikon app for use with their cameras. It is available on the Google Play Store (https://play.google.com/store/apps/details?id=com.nikon.wu.wmau&hl=en)
https://play.google.com/store/apps/details?id=com.nikon.wu.wmau&hl=en_US
Have you tried the Nikon App?
Well, yes, basically. It isn't just a function of shutter speed, though. The longer the shutter is open, the more light is let into the camera. If there is a lot of light, the shutter only needs to be open for a fraction of a second to get enough for a good picture. But if there is low light, the camera shutter will stay open longer, and this causes blur if the object/camera moves during this time.
So, the more light sensitive the camera, the quicker the shutter speed is, and the faster the shutter can close. The problem is most cell phone cameras are tiny, and let in very little light. To compensate, the shutter must be kept open longer to let in enough light.
You could consider getting something like the Nikon Coolpix S7000 from Amazon: $169 Refurbished or from Beach Camera: $149 Refurbished, which has built in Wi-Fi and NFC. This allows you to connect the camera wirelessly to a phone or tablet and directly transfer pictures and even control the camera.
Below is the app for controlling the camera. You can view the photos on the camera through the app, choose the ones you want, easily transfer them to your phone/tablet, and upload to social media.
https://play.google.com/store/apps/details?id=com.nikon.wu.wmau&hl=en
Edit: Another Option
The Sony DSC-WX350 is another good option and has better light sensitivity than the Nikon. The Sony uses the below app to control the camera from a smart phone.
https://play.google.com/store/apps/details?id=com.sony.playmemories.mobile&hl=en