Will A New Strap Affect A Watch’s Value?
Let's just assume that the watch you are talking about is, or may become, a collector's item. Most will not, but assuming it is, you'll want to keep all the original stuff. This includes box, papers, tags, everything... If you go to sell the watch and it does not include the original strap, then yes, the value will be reduced because not everything is original.
Having said that, if you have the original strap then just remove it and keep it. Some people remove original straps right away because they want to keep them in pristine condition or simply don't like them. If the watch comes on a bracelet - you'll certainly want to keep that. Original bracelets are much more valuable on collector's item, or even "new vintage" pieces that you might want to sell a few years down the road.