The heat exchanger looks like an off-the-shelf CPU heatsink with heat pipes. Something like this should work: https://www.newegg.com/cooler-master-rr-2v2e-18pk-r2/p/N82E16835103331 You can probably find something better but at a glance I would expect it to work.
Any fab shop should be able to make the cone for you, probably just from looking at the photos.
Also, make sure to attache the peltier's using something like thermal adhesive (also something you can buy at newegg). If its a non-permanent attachment you can use thermal paste like Artic Sliver (also from newegg).
Kinda like mounting a CPU?
yeah, there are even some companies that used to (dont know if they still do) make peltier based CPU coolers. Something like that would be super easy to source from.
Also, those crappy little "fridges" for your desk that can run off USB or wall power that only cool 1-2 cans at a time all use peltier's attached to a small heatsink and usually a small fan.
[edit] - This is basically what you are looking for but has 3 fans so the power draw would be higher. https://www.ebay.com/itm/193993145447?hash=item2d2ae47c67:g:lu4AAOSwlK1fVbH5&amdata=enc%3AAQAHAAAA4LDcTHcerPpkXx7p8MV%2FqiD4kuIIe%2B42w9zPmXctKiWrYR%2FjZDl9Fsfxa5ImQdt%2Bf%2FtmXD3GoasXs2cDS2sAWubrafSVAfeB3pzmq9M3aV4CB%2FOS7UsqXtQuSeHLzrdcITlyo5ALPs3qzO7nxVmaWNCIR2sQVe%2Fc8ZXAA7KeD9MNxfAzz5qGO6GoRmVoJyOvzy0uy6Jdd8XIJl4kjoGx%2FPKCeK5izqEhD7m7nUlqG%2B3JaN5hm35GM3mZ6ALz1LS3ML0PYsyPv7TjteqWxKH8yKCVHFQ0LkMCZaFfxsWItUcI%7Ctkp%3ABFBMote7icFg
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