I can't recall ever seeing a thumb push opener Lefever with a straight grip stock. I earlier offered the opinion that this gun probably did not originally have a straight grip stock. I based that upon the short tang trigger guard, and the fact that I had never seen a thumb push opener with a straight grip.
I believe all straight grip Lefevers had a different trigger guard with a very long straight tang. Earlier full pistol grip stock guns had a trigger guard with a tang that had a square end which ran all the way to the grip cap. If this is the original trigger guard, I'd think it was for a 1/2 pistol grip stock. However, the usual serial number engraved into the tang is not visible. It may not be original, or it may have been filed off, since it seems rough in that area.
I don't have reprints of all the catalogs, but the earlier ones seem to mainly describe guns as having full pistol grips with grip caps. Nichols & Lefever price lists offered mostly capped full pistol grip, with some 1/2 grip. Straight grips were not offered. We don't see straight grip stocks offered as an option in catalogs until much later. Of course, Dan Lefever would give the customer what they wanted within reason, so there may well be an original straight grip thumb push opener gun out there. Robert Elliot's books show pictures of some earlier Barber and Lefever hammer guns with the thump push opener system that have uncapped 1/2 pistol grip stocks. Unfortunately, most of the photos of thumb push guns do not show the grip area.
When it isn't possible to maintain 100% originality, I think it is never a mistake to at least try to maintain the original configuration. Since you will be taking your time before beginning to restock this, it would probably be best to do more research and spend time watching auctions of thumb push Lefever and Nichols & Lefever guns to see which grip style was predominately made and sold.