Honestly I wouldn't. I don't like this product and I think it's really predatory. There is no evidence that it works either despite their claims - if you look carefully it's clear they are only reporting on people's perception that it helped.
I don't think it will help with anxiety. If anything, I think it will make it worse. Stretching your vagina beforehand is nothing like it will actually be like in labour. When you're actually in labour you'll have all manner of endorphins flooding your body (not to mention the possibility of pain relief/drugs!) plus it is the culmination of all the contractions, all the work, the literal labour that you will have been doing for the previous few hours. It will not seem like as big of a deal as it feels right now. It will not matter as much as it seems to matter right now. You will be about to meet your baby.
Also, vaginas are not a muscle, it's more like a sphincter, similar to your anus. You can't just open it on demand like your mouth, it only stretches when it needs to stretch. This means that you definitely cannot "practice" opening it to the size of a baby's head and if you tried you would only cause yourself pain and potentially damage. This would not really help with labour - in fact it would probably make the possibility of tearing etc worse.
If you want to do something to help reduce the chance of tearing, I believe perineal massage has a very small proven effect. Also working on breathing type techniques to help you focus, relax your whole body, and slow down pushes when it gets to the time. But mainly I would speak to your midwife about managing the anxiety around the crowning stage, about pain relief options, and about any techniques you can do to help prepare.
This thread may also be useful for you to read through:
www.mumsnet.com/Talk/pregnancy/4230279-Really-fearful-about-pushing-actual-delivery-stage-of-labour
And this video may be helpful to watch:
Sorry I didn't see your post before.