While I doubt you will ever get it all out I think the majority will be removed. I don't think I would worry that much about a little paste on a paddle used only for travel. It's not like you will use it every day all year so the small amount of abrasive is unlikely to make a huge difference.

Remember that in another thread everyone is talking about adding a fine abrasive to the linen side of their strops which will be used quite often.

Tony