Is there a way to delete text in front of the caret using the iOS software keyboard? The small wireless hardware keyboard accomplishes this with a fn+delete, so there might be a way to use multiple keys to accomplish the same task in iOS?
Nope. In the stock keyboard provided by the API, a "Forward Delete" (as opposed to a Backward Delete/Backspace), none of the keys, nor combination therein, provide a Delete keystroke to occur. Your only option, as you now see, is to use an external keyboard to accomplish this.
Any other options would just be something else entirely. Like selecting a word, and deleting it, or using replace, etc.