I did this once for my Classic II. Though my second Mac was a PowerMac 6100. I used AppleTalk and copied all the disk images to my Classic II, then booted up from a startup disk. (I think it was the 7.6 Startup disk.) And ran the 7.5.3 installer from the Hard Drive. 
The question is how to get them to the LC475.... :-/ If your LC475 has an ethernet card then you could transfer the files through FTP.
Oh! I know! Do you have a PC anywhere!? (Shocking I know.
) You could use TransMac, a program for Windows that lets you read and write HFS/HFS+ images. (15 day trial, long enough for this. 
) You could get all the images onto a PC, run TransMac and burn them on a CD using the HFS format. Then pop the CD in your SCSI CD drive and TA-DA!
The question is how to get them to the LC475.... :-/ If your LC475 has an ethernet card then you could transfer the files through FTP.
Oh! I know! Do you have a PC anywhere!? (Shocking I know.
) You could use TransMac, a program for Windows that lets you read and write HFS/HFS+ images. (15 day trial, long enough for this. ) You could get all the images onto a PC, run TransMac and burn them on a CD using the HFS format. Then pop the CD in your SCSI CD drive and TA-DA!