You can set Kutt as your default URL shortener in ShareX app.

ShareX supports Kutt out of the box, you can find it under URL Shorteners in destinations settings.

You first need to make it compatible with ShareX. If you're using NGINX, then refer to this issue. Now get your API key from the settings page and edit the below info to add your key, domain and name:

{
  "Name": "kutt",
  "DestinationType": "URLShortener",
  "RequestURL": "https://kutt.it/api/url/sharex",
  "Headers": {
    "X-API-Key": "yourapikeyhere",
    "Target": "{\"target\":\"$input$\"}"
  },
  "URL": "$json:shortUrl$"
}

Copy the above code and open ShareX app, go to Destinations > Destination settings..., open the last option "Custom Uploaders". On this page find import button and select "import from clipboard". (You can also save the file in a .json file and import from file)

Now in destinations menu choose "Custom URL Shortener" as the default shortener.

Thanks to @nightah for configs.