If there are any numbers visible on the old filter, then somebody somewhere can probably cross-reference it. I'd try Cat forklift dealers and local industrial suppliers. If it's a canister-type filter, then go ahead and remove the filter and wipe it clean. You might be surprised to find visible numbers still on it. I've got lucky several times this way dealing with old obsolete equipment.
If you have to make another filter work, then just be sure to err toward getting a larger filter than necessary. Northern Hydraulics sells cheap hydraulic filter heads with varying flow ratings. I don't have any way of knowing exactly what flow that equipment pump would put out, but I am pretty familiar with similarly sized skidsteer loaders (Case, Deer, Bobcat, etc.). The smaller machines (similar in size and horsepower to that forklift) usually flowed 10-15 gpm. I'd be surprised if your towmotor flowed even that much. So just to be safe, if you go with a filter that's rated for at least 20gpm, then you'll be fine.
I rebuilt the engine in a similar forklift a couple years ago, but about a 1970 vingtage, I think. Had a 4-cyl. flathead Continental engine. We were able to get most of the parts from the Cat forklift dealership here in Wichita, and the rest from a machine shop that they recommended. No manuals were available, but I found all the critical torque specs on assorted parts supplier websites. Last I heard it's still running (used daily at the John Deere dealership where I worked).
This forklift had a clutch that was similar in design to what you'd see in a pickup, but the disk had different friction material... and it was a wet clutch. Had a separate reservior with a dipstick, with a pump to circulate clutch oil through a cooler. It was filled with ATF. Nobody could give us a definitive answer on what oil SHOULD be in there, so we just topped off the ATF with dex III, and it worked fine.
Can't tell you anything about the tranny and diff... I didn't mess with either of those. I'd probably pull the plugs and try to identify the oils by smell/feel. Odds are that they both take 80W90, but hydraulic oil is also a possibility.
I agree with others here that any AW46 hydraulic oil should work fine. As would AW32, but I'd probably go with the thicker oil since this is an older machine. Since this is a hydraulic-only application (no wet brakes or anything like that), you don't need anything fancy or specific... but UTF would also do the job. In my experience, hydraulic oils are not problematic when it comes to mixing. The only systems that I've seen that are kinda picky are those that involve friction materials like clutches or brakes.
Depending on how much water got into the system, you might have to change the hydraulic oil twice. I would just look at the oil after running it a while and getting it hot, then make a judgment call.