Sorry to be awkward, but the answer is probably No and Yes.
I don't think this is possible with normal midi. As far as midi is concerned, there is no 'tuning' adjustment, and this is really dependant on the device which is the destination of the midi commands. It is possible that your specific device may have a controller that might allow a small adjustment, but the amount may not be enough.
But, maybe Yes if you use SysEx commands, and there are specific facilities within the device to allow some sort of global tuning. You'd need to look into the Memory Map for the Midi implementation, for something like Global Tuning.
Leaving aside specifically midi, your keyboard (?) may have some sort of 'Master Tune' facility - I'm looking at the manual for my Yamaha MU90r unit and this has such a setting which allows an adjustment of +/- 102 'cents' where at 440hz 1hz is approx 4 cents. So this has sufficient range to do the adjustment you suggested. This Master Tune data IS visible in the Midi format/map, so in theory you might be able to use SysEx to change it, but the various examples of using SysEx do not include master Tune so I don't know how practical this would be. May be necessary to experiment. The specific parameters, and the addresses of them, would be quite different for your device.
Oh, I'm not sure that any such change could be 'permanent' Unless you leave the device on/powered-up. If you find you CAN do it with a SysEx command, then it would be easy enough to run this command at startup each time you use the system?