You'll be scooping up interstellar medium at significant kinetic energies.
There's two problems: The atoms that hit you will actually accelerate you away from your position (pressure measured in Pa), and of course they'll impose a radiation hazard as you absorb them (radiation dose measured in Gy).
Let's do some math. Let's assume an interstellar medium consisting of one hydrogen atom per cubic centimeter.
This gives a density ρ = m/V = 1.7e-21 kg/m³.
You'll scoop up the ISM at dm/dt/A = ρ·v = 1.5e-13 kg/s/m². Note that this depends on the area of your body that is facing into the stream; you might want to go head-first or feet-first depending on if you're still planning to procreate.
The pressure that the ISM exerts on you is p = F/A = dm/dt/A · v = 1.3e-5 Pa.
This is pretty negligible, you won't even feel it. At an exposed area of 1m² and a mass including the EVA suit of 100kg, the acceleration is just 1.3e-7m/s², enough to displace you by less than a meter in one hour.
The radiation hazard is another thing, though. The kinetic energy at relativistic speeds is calculated by multiplying the relativistic gamma factor, minus one, with mc². The relativistic gamma factor in your case is 1.04828.
The kinetic energy of the mass stream is calculated by P/A = (relativistic gamma factor - 1)·dm/dt·c^2/A = 653W/m². This is half the power of solar radiation as felt on earth. Which is a lot.
The radiation dose is calculated as energy absorbed per body weight: Assuming a body weight of 80kg and an exposed area of 0.5m^2, D/t = P/m = (P/A)·A/m = 4.08Gy/s. 921
This handy table tells you what will happen to your spacewalker.
* They'll pretty much immediately feel the extra heating
* After 2 seconds, their biology is damaged beyond repair with a life expectancy of 2-4 weeks, and "rapid incapacitation" sets on
* After 7 seconds, they'll experience "Seizures, tremor, ataxia and lethargy", and their life expectancy has dropped to 1-2 days
So... without some sort of shield there's no way a human could do a spacewalk.
however, these levels of radiation will not only affect spacewalkers, but everybody on the ship, so the ship will likely have massive leaden (or similar) shields at its front. As long as your space walkers would be in the "shadow" of the frontal shield, they have nothing to worry about... apart from accidentally drifting into the death zone...
Of course the radiation levels outside the ship would still be elevated because
* the ship's hull provides some additional shielding
* some particles can be scattered around the edges of the shield which would lead to a gradual increase in levels the closer you get to the "edge" of the shielded zone, especially near the rear end of the ship.
but if the inside of the ship is shielded well enough to allow humans to live a normal live and life, they should be able to survive outside for a few hours without problems.
P.S. I think the leaden shield is actually doable in practice. I'm not sure how to calculate its thickness, but it will be probably ~50 times the mean free path of 0.3c hydrogen atoms in lead, whatever that works out to. You could make the shield out of Unobtanium which I hear has excellent properties in that respect. Unobtainium shields may even be light enough to be worked into the fabric of the EVA suit... but note that you'll still need to cool them, and since your visor can't be made of it, don't you ever stare into the direction of oncoming death. 947