Here's a sort-of-realistic answer:
-snip-
Uh... nah.
I like the thinking here - it's creative - but to imply it's even vaguely realistic or feasible with our technology is somewhat misleading... at least the way you were talking about it. What you're describing is an Orion Rocket and was originally conceived in the late '50s. Upper estimates for the speeds attainable using this type of method (nuclear pulse propulsion) range from 5% the speed of light (if retaining fuel for deceleration at the destination) to 10% (if not.) Reaching 35% the speed of light using this method just flat out isn't possible -
especially with a manned spacecraft due to the limitations introduced by the human body's capacity for enduring rapid acceleration. Sure things like the Oberth effect might help a wee bit - but consider that the current record speed for a spacecraft is 0.000234 times the speed of light (set by Helios 2) and you'll realise that it just isn't going to have any sort of actual impact when we're on the interstellar scale.
Now - I don't disagree that were one to have a fully built Orion Rocket in space that it could work extremely well for the purposes of interstellar travel... but one must consider how you actually construct the rocket and get it to space in the first place:
1. Dyson calculated that it would require a nuclear detonation every three seconds during acceleration to attain the cruising speed. This would require 300000 nukes to be aboard. Dumping waste and fecal matter ain't gonna change shit about the metrics of this thing dude. It'd be scary huge.
*2. Using chemical rockets (current method) to get the rocket to space is inefficient as fuck - and we can't use the rocket itself to get out of orbit because of the International Test Ban Treaty of '63.
3. The cost. Oh jesus the cost of construction. The size and weight of this thing would be colossal and even obtaining enough materials would be challenging (where do you expect to find enough nuclear material to make 300000 nukes?)
* Side-note: that's actually one of the benefits of the Orion design. You can just make the ship fuck-off massive and have a crew of like 200 because it has to be so big anyway. You don't have to be totally anal about losing every tiny bit of weight like they do now with chemically propelled rockets.
Anyway I've ranted enough. It's a super cool idea and could definitely be feasible in future - but right now it simply isn't. Personally my favourite theory for interstellar travel is either the usage of a solar sail or - of course - using matter-antimatter explosions instead of nuclear ones.
This is a really really good article discussing potential methods of interstellar travel. Check it out. :D