Hi @Mendocino,
Welcome to the Community!
Yes, you will only need to integrate WooCommerece to your subdomain, as that is the one that that has all the necessary data you will want to collect. If you are looking to use forms you would use the same public API key for this. Additionally, if you want to run signup forms to collect subscribers on their main domain, all you will have to do is manually add the Klaviyo.js, which will include your public API key, for your Klaviyo account to the main domain.
Thank you for sharing your question with the Community!
-Taylor