Replacing scales, what thickness ?

Hi there, I just received my first vintage Straight razor in the mail today.
It's a Robinson and Thompson and the blade is very nice but the scales need to be replaced.
They look like horn and the metal wedge is also part of the scales, see pics.

The scales seem quite thin and delicate so I would like to know if generally speaking, do you
match the new scales to the exact thickness of the old ones or do you sometimes
make them thicker or "chunkier" ?

I notice that some wood razor scales are sold in 1/8", 1/4" and 5/16" thickness.
Do you gents have a preference when buying wood that will be used for razor scales ?
Any info will be greatly appreciated.
Bongo.

I start at 1/8 and thin to balance from there...

1/8 is a good start, unless you don't mind resawing and planing thicker blanks, otherwise you will have a butt load of sanding ahead of you; you wil use a lot of sandpaper, and yeah it aint expensive per se, but it aint free either.

The scales you're looking at have dissolved, as it were, over time so you're not looking at the original size anymore. If you're new to this, follow the general shape of the original scales but find out what is comfortable in your hand as you're shaving. As Glen said, find the balance point of the scales and the razor.
I don't know what tools you have available or your woodworking experiance. I have a small block plane, a coping saw as well as a sander. You'll never know how small is too small until you've gone past that point at least once. You can always sand a little more wood off but you can never put it back on.
Whatever wood you choose or it's thickness, I would suggest that you start with a common hardwood from your area. That way if it doesn't turn out as you like, chuck it and start over.

Thanks for this guys....DGilloon, yes, the scales have dissolved over time.
I didn't think of that, and the idea of using a small Block Plane for thinning wood is brilliant !!
Once again, why didn't I think of that ?....I'll be buying one when the hardware store opens.
Thanks again.

This video may help.

Making straight razor scales with a minimum amount of hand tools.

making straight razor scales with a minimum amount of hand tools - YouTube

This is a great video, thank you pointing me in the right direction !!