As far as Bowser is concerned, you may not want to approach with bairs because he can shield to dash grab a perfectly spaced bair and in that case he may as well have a tether grab because his dash grab, like all of his moves, is quick with a lot of ending lag. Also, a grab means a lot for Bowser what with his CGs(though DK is the hardest to ground break CG). Also, the flamethrower is extremely underrated and he will deal massive damage on you by predicting your DI so he can keep you away with it. As far as aerials go, he probably won't be challenging you there although his fair has underrated range as well. It has enough range to pop you after an avoided bair. He can also move around a stage faster than you, if you can believe that. He can also have some fun with your recovery. He won't gimp you but he can deal a lot of damage.
As for Snake..again it's just up to you to avoid his traps while still pressuring him. Great trap placement is hell for DK but that's not so easy to achieve with the monster running you down. Just abuse down B, not much Snake can do against it if you use it intelligently. Your weight also doesn't mean much to him because he racks up damage oh so well, but you'll notice if you play smart and use your down B to nullify his entire ground game, avoiding his projectiles means you won't take any damage. The only thing I find hard is getting the kill with anything but giant punch because of Snake's amazing tilts preventing you from getting many smashing opportunities.
But all of this doesn't mean it will be easy by any means, just that DK has an advantage.