Removing an unkown wood stain

So I purchased a new desk last weekend, and it needs a bit of restoration before I can use it.

I would estimate it to be around 80-100 years old (but could be older). I am fairly sure the finish currently on it is a varnish. To begin with I have given a quick sand to the drawers and an inside panel with an orbital sander (I tried removing the finish with a Varnish stripper, but this didn’t have great results, some of it came off, but not a lot. this is the result so far (with the sander):

As you can see, the existing stain is quite deep into the wood, am I best of just persisting with sanding to take it back to its original surface?

Once back to the original surface I plan on re-varnishing with an Oak shade (so lighter than the old finish). Due to the age of the desk I imagine the current finish is an oil based product, so I will have to-refinish with an oil based product again (unless I manage to take it all back to its original surface)

This was the desk before I started (the picture from the Gumtree Advert,you can’t see from the picture, but it needs a few panels filling/re supporting and the finish is much darker in person):