FYI: That's a short style side bed (aka wrong bed) the same as the 57-60 F100's. Hope someone can help you with the location of a repop or maybe a used one in good shape.
Stay safe and hope you're back home soon.
Ford truck history lesson: in 1961 Ford introduced a new pickup with an integrated cab and bed (one piece) now known as the Uni (Unibody, although it technically isn't). Since these were "work" trucks the customers/owners complained of flexing under load causing the doors to pop open or split the sides. To stem the complaints, sometime in 1962 they added the 57-60 bed (as that was all they had designed and in stock) to the cab and frame used on the Flare side trucks and continued this usage until the end of the 63 model year. The Uni was also discontinued after 63 and replaced with the redesigned 64 Style side beds. The bed is "affectionately" known among Ford enthusiasts as "wrong beds". They are "correct" for the trucks, but look "wrong" as the lines of the bed don't reflect the lines of the cab.
I think it would boil down to personal preference. At first I wasn't a fan, but the WB is growing on me, especially in a dark color such as black or dark blue). That said, I plan to replace the WB on my crew cab with a Flare side bed.
IMHO it wouldn't affect the "value" much if any, unless you were striving for a 100% correct restoration. "Value" is what someone is willing to pay you for it. You will quickly find out that you will have more money in your truck that you could possibly expect to get out of it on a sale.