I’m going to preface this by saying that veiling is not a requirement in Hellenic polytheism, just to be clear so no one reads this and gets the idea that they should be veiling, or that they have to, because that’s just not the case. Some specific branches and groups may require veiling, but none that I’ve heard of (doesn’t mean they don’t exist, just that I’m unaware of any branches of Hellenic Polytheism that require veiling). Veiling is always optional for Hellenic Polytheists, and a personal decision.
Moving on to the content of your question now. My theory on why veiling keeps off miasma is that it’s a physical reminder of the theoi and our devotion, and that reminder can be used to help us distance ourselves from things that generate miasma. Not everyone feels that way, but that’s how I figure it works. So, by that logic, devotional jewelry, veiling, hair binding (which includes braiding), and things like devotional tattoos can all fulfill the role of reminding us of the theoi and thus distancing us from miasmic events.
On a side note, the way I veil for work is to wear a simple headband. I’m not comfortable veiling at my workplace in a way that may raise questions, so I’ve got a few different headbands that I can wear. They’re the kind you can pick up at the hair accessory section of any store, and they fulfill my veiling needs in a subtle and comfortable way. You may want to check that out, and start with something similar when/if you work your way up to veiling.