There aren't any statistics on this. While there is a chance to transmit hsv1, the chance that you'll get a cold, flu or something like strep throat are much higher.
Do you know if you already have hsv1? Have you ever been tested? Many people have it, and most don't know it as most never get cold sores. If you're curious, ask your doctor for a type specific IgG blood test.
I appreciate the response. I had looked up online about this and kept finding different answers. Some saying you can contract it from an inanimate object, while others saying you can't. So I came here, thank you.
I've never had an outbreak my entire life so I assumed that I didn't have it. I haven't been tested for it, considering now after this situation.
Okay, so not getting it from an inanimate object has some layers to it.
You won't get it from a door knob, hand rail, furniture, toilets, etc. You can get it from things that are wet that someone else has just used when you use it - sharing drinks/straws, utensils, cigarettes/joints, lipstick/lip balm, etc. In a lot of those, conditions have to be right - if you use a fork an hour after someone else did, you probably won't get it. If you use it immediately after someone who has an active cold sore, you have a much higher chance.
Hope that helps. But really, it's so much easier to catch a cold, the flu, strep, etc., so sharing is never a good idea.