28x1.35 turbo tyre

Please help!

I'm a total newby and don't understand much. I've just got a turbo trainer the tacx flow and wanted to get a turbo tyre for noise reduction and my current tyre isn't the best. I've got a cyclo-cross bike with a tyre size of 28x1.35 and wondered if a 700x23 turbo tyre would be suitable? I'm just struggling to find any the current size?

Sorry if this has been asked before I've just not been able to find anything concrete advice wise.

Many thanks
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