Blow, wash or vacuum all dust and dirt off of the optics before wiping with any kind of tissue. Otherwise the material on it will just be a grinding compound. Fold your cleaning tissue into quarters and use each quarter only ONCE. With every wipe turn the tissue over and use a clean area. Do not use the same tissue surface to make more than one wipe of you'll just be using the girt and grime picked up on the first pass and grinding into the surface of the optics on the second pass. I really can't advise you about a safe cleaning liquid, that all depends on what the optics are made of and what coatings that they have on them. The manufacturer needs to advise you on that. (Yes, I know that it's an old item and the manufacturer is probably long gone.)
"I'm guessing generic lens cleaning wipes would do the job? Like eyeglasses stuff."
Yes, and do NOT use ordinary paper towels for this kind of cleaning, the fiber in them has a lot of abrasive material remaining it in. Always use tissues made for optics or lens cleaning. That apples to eye glasses as well.