the slim still has ps1 compatibility I'm pretty sure (I mean, the PSP has it, so why would they remove it from the PS3 since it's software emulation in the first place?)
also all ps1 games work with old saves (PSN downloaded or not) since you have to "mount" memory card images inside the ps3 itself
although it is actually impossible to get saves from your PS1 memcard to your PSP without having a hacked PSP and an unofficial windows program to dump memcard images with the memcard adapter