Will non-catted exhaust fit a TR with a cat ?

A picture of the exhaust system would help, but it should likely fit okay - if you remove the Cats from your TR. You will need to keep the Oxygen Sensors so hopefully there are bungs for installing those. But you will not need the Thermocouple Probes anymore, these can be removed.

 

I would say "no" as the exhaust headers are quite different -- the non-cat headers are much longer with not staggered outlets:

non-cat:
https://www.ferrariparts.co.uk/diagram/ferrari/testarossa-tr-90/019-exhaust-system-(for-b1-rhd1-version)

with precats & cats:
https://www.ferrariparts.co.uk/diagram/ferrari/testarossa-tr-90/020-exhaust-system-(for-us-sa-and-cat-version)

A couple of other things that might be issues:

I think the rear exhaust grills are also different -- i.e., the tailpipe outlets might be in different places, but haven't looked for photos.

and

The 4-piece non-cat silencer may interfere with the charcoal canisters on a US TR.

 

As Steve points out there are major differences between the Euro and USA exhaust systems - you can't mix-n-match these. I was assuming both systems were for the same market....sorry...... :-/