Hi Kitty Magenta, congrats on your pretty pochette plus strap, I wanted to encourage you to keep the Eva strap, IMHO it's the best strap and it's genuine LV, I've read that this strap is sold at LV for $240 if sold alone, and for $120 if it's a replacement part for an Eva, I think it was fortunate that you were able to get the strap for $120 without owning the Eva, this is my understanding after reading posts about this, someone correct me if I'm wrong on the pricing for this strap.
The untreated vachetta is a little vulnerable right now because it's new, but it will be safer to use once it starts to develop patina. When I get mono items I like to leave them on my dresser for a few days or weeks to receive some indirect sunlight, and after some time I start to use them and they don't get water spots or stains like fresh new vachetta. You could also treat the leather with AppleGard or Kiwi, if you go into the FAQ's section of this forum you'll find several methods to treat vachetta to avoid spots, then you'll be able to use your strap without worry in any weather.
I consider the leather strap to be very casual and I would use it for daily wear, I wouldn't save it for weddings unless it was a casual ceremony. I hope this helps and you're able to use your pretty pochette as much as possible, enjoy!