Can I delete an app without downloading itunes?

Delete from where ? You can delete a downloaded app from your iPhone directly on the phone by pressing and holding it on the phone's home screen for a second or so until they start to shake, and that tapping the 'x' on its top left corner.

To hide (you cant permanently delete them) an app from the cloud so that it doesn't show for redownloading you need to use a computer's iTunes : Hide and unhide purchases in iTunes or iBooks on your Mac or PC - Apple Support

(On the current version of iTunes, downloaded today, I'm not getting the Purchased link as described in the iTunes step 3 on that link, I'm having to go to Purchased under Quick Links on the right-hand side of the music store homepage and then selecting apps.)