FoxholeAtheist said:
Buy the RTAK or Swamp Rat knife you want, then spend about $25 on a good folding pruning saw.
I concur with FoxholeAtheist's recommendation. Another downside is that the sawback knifeblade may well chew at your baton while being beaten through branches to get at dry wood on the interior. As he noted, a dedicated saw is much better at its job than knifeback saw teeth.
Folding pruning saws range from under $10 to the neighborhood of $60 or more, depending on how rigorously you shop and how important it is to have brand name product in your pack/pocket. My folding pruning saw choice for "bang for the buck" is the Tashiro Folding Pocket Saw for $28 plus shipping. One of the features of this saw, as well as many of the other mid- to high-end saws, is that you can replace the blade readily. Search here on BFC for comments on the saw.
On the lower end of your $200 window, I'd recommend a Ranger Knives RD-7 ($100) or another vote for the Becker BK-7 ($50) or BK-9 ($60), a home center folding pruning saw ($20), and a Mora style knife from either
Kellam Knives S-series models ($13) or else
Ragnar's Ragweed Forge Swedish knives ($8-30). The one I like from Ragnar's is the Swedish Army Knife model #760MG for $11.
SAK's also make a decent small knife, but I like them more for their extra tools. Any folder, including a SAK, loses primacy because of the relative weakness of the joint and the crannies where gunk can accumulate.
If you want to use ALL of that $200 or a touch more, I'd recommend the Swamp Rat Camp Tramp ($125) for the big knife. I'd change the small knife recommendation from a Mora to a Spyderco Moran Featherweight ($65), Benchmade Outbounder ($65 in 440c, $75 in D2), Swamp Rat Howling Rat ($88), or Cold Steel SRK factory second ($50).