I think that the 4x would would great on your Hawkeye, if you want to put it on there. It has plenty of field of view for any shots you should be taking at close range. It has good eye relief too, for those "warm" loads with heavy bullets you might try in your .358.
The real question, IMO, is whether or not you think that you'd like a different scope on the Model 88? If you like how the Buckmaster looks and feels on the 88, I'd leave it there and get the scope for the Hawkeye. I'm a fan of compact scopes, and I think that I'd get the Nikon ProStaff 2-7x32 myself.
You say you can only afford one scope, but have you considered selling the Buckmaster? Then you could get two scopes if you want to have a variable power scope on each rifle. If you look at SWFA's Sample List, you can get some good deals on ProStaff scopes (as well as other brands). Also look hard on ebay as well. I've seen the 2-7 ProStaff's selling for as little as $100 on both sites, both new and used.