Candle sticks glued in between
Even cooler if you decorate the cake to look like a record.
I would buy 1” diameter wood dowels, cut to length and then drill holes in the ends for dowel sticks.
The bottom tier would have a screw & washer through the first dowel, in the record hole. I’d put cork or felt pads on the bottom of the base record to make it easy to pick up and not be tippy from the screw.
The other tiers would have their dowel sticks wood glued in.
The top tier could be screwed in, like the bottom, depending on if you want a finial on top.
You can buy the kits from amazon for the central risers
Can be made out of different things. Concept would be the same with records.