Yes you can use an adapter with no worries.No speaker level inputs on your sub?That would be another option.
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Should be no problem at all, the cold signal should be connected to the shield at the RCA end, that way you get some of the benefit of the noise cancelling. If you don't mind soldering then they are simple to make by cutting the connector off a balanced cable at one end and replacing with an RCA connector.
If the adaptor boxes are powered then you'll probably be getting a true differential signal which will mean you'll get an extra 6dB of gain at the input to the sub.