Speeding up a recording, and then re-recording... [SOLVED]

I am on Windows 7, and Audacity 2.3.3.
Someone sent me some old family interest 78rpm records. My vinyl deck however only has 45 and 33rpm. So i played the 78’s at 45rpm and recorded them in Audacity. This worked fine. Then in Audacity I see that I can ‘speed up’ the playback of the recording - so I used this facility to speed up the playback to 1.73 times speed. This worked perfectly. I can play the recordings at this speed and they sound OK.
Each recording I have saved to .mp3, .wav and .ogg format files - to hopefully ensure I dont need to play the 78rpm records again!
Question: Can I re-record these recordings, so that they are permanently at the ‘correct’ higher speed?? I sort of need to play (at 1.73 times speed) and record at the same time?? I assume (hopefully) this has been done before?
Any information welcome. Thank you.

Tim Ecott.

Rather than doing that, use the “Change Speed” effect. It has settings for standard record speeds. Change Speed and Pitch - Audacity Manual

Thank you. I have found this facility in Audacity. Case now closed. I have made my 78rpm record copies.