how to maintain high frequencies when recording from old cassette via cable to computer

This isn't an Audition issue - Audition records faithfully what it is sent from your sound device, and there's nothing that can be altered about that. The key to getting good high frequency response from old cassettes lies entirely in the player you use. Most 'normal' cassette decks used a single head for recording and playing, and there's a massive magnetic compromise involved in that - you need a wide gap for effective recording saturation and a narrow gap to be able to resolve higher frequencies - rather perversely, they record fine with a wider gap.

So the solution to keeping the HF response - and I'm afraid it's the only one - is to use a three-head machine with a dedicated playback head to replay your cassettes. I use a Nakamichi LX5 for this purpose, but good, serviced ones are now fearfully expensive. Most three-head decks will give you some advantage though, although the Naks (any of them) are universally acknowleged to be the best. You are up against the Laws of Physics with this though - you really can't get around this any other way.

Even hiring or borrowing a suitable machine for the job would probably be worth it - it's often quite amazing how much quality there is on old cassettes when they're played on a 'sympathetic' machine.

There are some other things you also need to do - check the azimuth adjustment on the machine you use - that makes a huge difference to the amount of HF response you get, and also make sure that the entire tape path and heads are clean. Spooling the cassettes end to end before playing them is also a very good idea if they've sat around for ages; that will reduce the amount of print-through.