I totally agree here, also trying to match it can be difficult but not impossible just take your timeIf the table is as old as you say, it's likely the inlay was glued in with hide glue. You can heat it up with a heat gun and the glue will release. What I do is assess the damaged inlay and if need be just remove what's bad. At 1/16", it's pretty small, and hard to handle. I use an X-Acto knife with a #11 blade, and scarf cut what will remain, and do a matching scarf on the repair. That knife setup can be used to work the veneer out. You have to be careful not to damage the border wood.
If you remove it all or just parts, you'll have to clean out the area before gluing new veneer. You could use yellow glue, or hot hide glue, and apply with a wood toothpick. With the color of Satinwood, the old may not look like the new.