You have lots of options here, many of which depend on whether you are prepared to spend real money on a proper commercial 78rpm external equaliser. This does not have the same characteristics as an RIAA equaliser as used for vinyl (33rpm) disks.
There are 78rpm equaliser DAW plugins you could try after you have rate-corrected the recorded file by 1.73 (from 45rpm to 78 rpm). Note that rate correction is different from pitch correction, as you need to scale the time as well as the frequency.
Alternatively, you could use a standard external analogue equaliser after the rate correction as though it were an external effect unit. My preference, though, would be to make your own equaliser with capacitor values 1.73 times greater than those in the 78 rpm published circuits and record through that. The rate correction would then be purely to correct the tuntable speed.
There is lots of advice (both good and bad) available on various web sites about 78 and 33 rpm disk transfers. The Danish company Vadlyd is a good starting point.