AutinHing, I was looking for a similar finish update for my new travel uke--just a little shinier, but not glossy. After reading some debate in this and other forums, I picked up a bottle of Howard Feed-n-Wax Wood Polish & Conditioner (
https://www.howardproducts.com/product/feed-n-wax-wood-polish-and-conditioner/). It's one of the brand name products that has the beeswax, carnuba wax, and orange oil combinations. Even better I could find it in my local hardware store.
I lightly prepared the neck, back, and sides with 0000 steel wool, then used a soft cloth (an old worn out t-shirt) to apply the product. Waited 20 minutes as directed then wiped off the excess and buffed the finish with another scrap of the aforementioned t-shirt. It turned out great, and I repeated the process on the top.
If it's not too late (or for others reading this post and learning that what-to-do's and what-not-to-do's of DIY uke improvement), I'd highly recommend this option.
I wish you all the best and much enjoyment with your newly refinished Martin.