You will need to get a shorter axle or shorten the one you have. If you shorten the one you have, leave a nut inboard on the end you are going to cut (e.g. with a hacksaw). Calculate the required length to cut off by the difference in length of QRs, so in you case 9mm shorter. After you cut the end off, chamfer the cut end with a file or grinder, then unscrew the nut to clean off the threads.
With the shorter axle, delete an equal length of spacers at each end and check the centering of the wheel in the frame; adjust if needed via the cones. Make sure you leave enough space on the drive side that the chain doesn't interfere with frame when on the small cog. Unlikely but possibly the wheel may need to be re-dished.
If the threaded end of your existing QR has enough threaded length, you may be able to shorten it as needed also.