Well, the main feature of Cobra is mounting disc images - before that (and its clone Mamba) it was only PS3 backups with that obscenely inaccurate overmount method (GAMES/folder type) and custom packages
Table of contents... a... piece of data on a CD which lists the start position of each track and little more information
Consider that the CD was invented as an audio-only format, while the sound is digital most concepts involved are closer to tape or LP than computer files, for one all seek operations are not guaranteed to be accurate to the sector and a disc should be playable start to end ignoring all track/time markers (which are found in, annoying to read and write, "subchannel data"), obviously a lot had to be changed/supplemented to make data discs possible
Even the PS2 has config files for PS1 mode (which of course resulted in the first softmod for the PS2 bios, the Independence Exploit)
But most are integrated into the emulators themselves, I don't think there's much interest for them unlike the ps2_netemu ones (PS2 on PS3 may be inaccurate especially if you don't have a CECH-A or B, but most PS1 titles work out of the box all while the PS3 doesn't support the most common video modes of the PS1 and sucks over triple the power...) and this includes the lack of features to load external ones (as if the format was understood...)
Irisman should have somewhere per-game options, for PS1 titles you can select an emulator there (I didn't like it much because apparently it applies various patches I didn't want?)
In Webman Mod you can select ps1_emu or ps1_netemu from the main settings page, IIRC