Bright suns, Megan! I am so glad your interplanetary travels will bring you to Batuu. I happened to be in the Outer Rim today and was able to get data concerning the transportation of artifacts for your question.
There are three locations in
Star Wars: Galaxy’s Edge where you can ship your droid and lightsaber back to your home planet. These include
Dok-Ondar's Den of Antiquities, the
Droid Depot and
First Order Cargo.
A Cast Member at Droid Depot provided some information on the credits required for shipping, with the caveat that prices vary based on the items and destination and may change. If shipping to the territory known as the United States, the cost may be around $18 to transport a droid and $35 for a lightsaber. If you ship both together, you could save a few credits. Again, this is just a recent estimate, but hopefully, it is close enough to inform your planning.
I hope the Force is with you in your travels. If you venture through
Star Wars: Rise of the Resistance, I recommend taking any interrogation seriously. I laughed when an Imperial guard was trying to ascertain the location of the Rebel base. He did not take it well. But rebellions are built on hope... and maybe a bit of laughter, too.
May the Stars Light Your Way!
Jana