I'm not entirely sure for your question whether you are trying to avoid the verb or avoid the entire clause. If you insert the action clause in the sentence, the ing verb is the right way to do it and anything else is going to sound forced and ugly.
However, regardless of the ing verb issue, mixing dialog and action like this tends to confuse the reader. Writing is all about focus. It is about directing the reader's attention to one thing in particular. If you mix dialog and action like this, the reader's attention is split between the two.
Dialogue is one of the most intimate and revealing of human interactions and it deserves our full attention. You will notice that when dialogue appears in most stories, it usually appears as a long sequence of speeches with little more than speech tags to identify the speaker and an occasional adverb to indicate tone. This lets the dialogue be the dialogue, and lets the reader focus on the dialogue.
It can be tempting to want to mix action into dialogue because that is how real human speech often works. The conversation is not carried by the words alone, but by actions such a pointing, and by facial expressions. However this kind of thing is difficult to reproduce on paper, where these motions have to be described in words, which take far longer to get the idea across than the motions themselves. For this reason, and because real speech is usually fragmentary and repetitive, fictional dialogue is not speech. In dialogue, the words are for more orderly and structured than in speech and they carry far more of the meaning.
You may use bits of vocabulary or diction to hint at the sound of real speech, but these are just decorations. Dialogue remains quite different from actual speech, and mixing too much action into dialogue just tends to slow it down. Actions in speech are simultaneous to words, but have to be described in series in dialogue, which gives the impression of them happening one after the other rather than simultaneously. Notice in your own sample how there feels like a long pause between each character's speech while the action takes place.
There is also the case where dialogue is incidental to action. In these cases you don't want the reader to focus on the dialogue but on the action. In these cases it makes sense to run the dialogue into the action, and even to avoid breaking it into a separate paragraph. In these cases, the use of the ing verb to tie the words to the action is appropriate, but you may want to do it the other way round, putting the essential action first and tacking on the incidental speech tag with an ing verb:
The lieutenant ran down the dock in a hail of bullets shouting "Cast off! Cast off!"
This seems to put the emphasis in the right place compared to:
"Cast off! Cast off!" shouted the lieutenant, running down the dock in a hail of bullets.
So, decide if it is the action of the dialogue that you want the reader to focus on in this scene. If it is the dialogue, move the action away from it. If it is the action, put the action first and make the dialogue incidental to the action.