Teak veneer is $$$; that Oakwood link will show you that. Actually, Oakwood has a wide selection of exotic woods in different cuts and you might want to peruse the selection and opt for a different wood. There are so many beautiful choices available.
Those cabs could be bondoed and sanded to provide a solid, flat substrate to bond to, so removing the old veneer is not necessary, but the time and materials cost could run well over $700+ easy and far more if a second sheet is needed or you want them to finish it. I see they don’t flow the grain over the top, so you probably can get by with a single 4x8 sheet if you skip the backs, which is a very common thing in furniture.
FWIW, that Oakwood link is to veneered panels for construction, not sheets. Here’s a link to teak sheets that are what you need for your project.
BTW, you need to pick the sheets yourself, as a random online order choice may not meet your expectations as color and grain vary quite a bit.
Shop premium Flat Cut Teak wood veneer sheets. Available with 10-mil, BFV, or PSA backings. Need Teak Plywood? We also offer Teak bonded to Plycore panels for marine cabinetry. Order online or call Oakwood Veneer at (800) 426-6018 for expert advice.
oakwoodveneer.com
Good luck and keep us posted!!