Coming out letter to parents while they are away?

My parents are going on a business trip for 1 week in July. My thought was to write a coming out letter to them and sneak it in their luggage when they leave. Yes, I still live with them.
I thought this would be a good way to do this because:
1. I will be able to say all I want to say that I may forget to do in person
2. the anxiety of seeing the initial reaction in person (I know they will be probably have the most emotional reaction). my sister (who knows) warned me this will hit them hard because I don't meet the typical gay stereotypes, so it will be a shock.
3. I feel the time apart might be a good way to help it sync in.

Although my parents are catholic, I feel in my gut they will come around to me being gay, but I think it will take them time. Homosexuality actually was never a topic really discussed in church ever (I used to have to go with my siblings every Sunday growing up, my parents don't push it on us though now). I live in a very liberal city.
Although the thought of them kicking me out still wanders in my mind, I think my siblings (all older than me and have their own places) would be very quick to back me up and I am very close with the people my parents see on a regular basis. I have done a lot of projects for people at my parents office and know a lot of the people there. So I just feel at the very least, it would be bad for business.

I could be wrong, what do you guys think? I am still new on this journey, so maybe I am completely off track with this.

Btw, for those that want to ask why I haven't moved out. I am in my early 20s and trust me, it is something I want to do soon. I am saving up and paying off debts.

Thanks for taking the time to read this.

 

Thanks for the kind response. I was not aware of PFLAG until now, so that definitely helps!