Non-blocking SoftwareSerial.Write
In short, you don't.
The SoftwareSerial implementation for AVR doesn't have an outbound buffer at all.
It just turns the interrupts off during each character outbound and it sends them all immediately.
This means a call to SoftwareSerial's write simply will block until all of the data you've tried to send has in fact been sent.  If you can't afford to wait for your data to go out on the TX line now, then it's up to you to send it later when you can afford to wait.
SoftwareSerial has no flow control.  When you write(), the data is sent out on the TX pin regardless of whether anything is present on the other side of the connection.  And when present, the data is still transmitted regardless of whether other side considers itself &quot;ready&quot; to receive.  There's simply no feedback from the receiver to tell the sender to stop.  So SoftwareSerial itself will never block owing to these things.