It’s fairly unlikely that the conrod is the only casualty if it’s been run with no oil.
You could be extremely lucky. However, I’d be checking everything, piston, bore, big end, gudgeon pin, mains for scoring and wear along with the valve gear before embarking on what could be an expensive exercise.
I’m not familiar with the mower you’re referring to but purpose-built motors from major manufacturers tend to be “parts-bin specials”. That is they often build them up from their existing range. So you may find that there is a lot of commonality with other models which will let you get hold of parts.
Another, possibly more cost-effective, option is to locate the same (or similar) mower with a good engine but other damage and make one “good” mower out of two. There are plenty of people on here who do this sort of thing. It’s often the only way to retain the originality of the equipment if that’s what you’re interested in.
It can require a little patience but if you take broken mowers that would otherwise be going to scrap and make a good serviceable one then that’s got to be a good outcome any way you look at it.
