I hear that universal links are more secure than the application URLs and want to exclusively use iOS Universal Links.
The Twitter Card documentation seems to only emphasize app links.
Can I use deep linking with Universal Links in Twitter Cards?
I'm not quite sure what you mean by 'secure', because both Universal Links and URI schemes result in the app launching directly in response to a user action on the local device. Perhaps you mean that Universal Links solve the potential issue where the URI scheme of a popular app is hijacked by unscrupulous characters?
In any case, Universal Links and Twitter Cards currently don't play nicely together. Universal Links are handled at the OS level, which means Twitter wouldn't be able to do any sort of tracking and attribution on those events. Instead, they use URI schemes to open the app and manually handle the fallback behavior for when the app isn't installed.
You can find a partial list of apps that currently support Universal Links here