I have a Wise card, but basically never use it - I just can't see the advantage over my bank debit and credit cards.
For example, Wise is offering USD1.347 per £1. My bank exchange rate is USD1.35 per £1. So basically the same. If I use it to transfer money, Wise charges a fee, but my bank does not. And I can hold multiple currencies both with Wise and also with my bank.
But it is basically a fintech, very similar to Revolut.
Wise will issue you a card (in the US it will be Visa, here in Singapore it's Mastercard). It will behave the same way as any normal visa debit card. Same risks etc as using your standard bank cards.
The safest way is to pay by phone. For public transport you can keep is locked even when you tap it, and it can't be used for anything else, even if you lose the phone.