Nope, the big problem is getting propulsion that would cut the trip down to weeks instead of a couple years.
A 2 year trip in deep space would cook the astronauts like filets with the radiation.
They've had astronauts spend up to a year on the ISS with no filet-like symptoms.
How about some hard numbers?
What specific kinds of radiation are you speaking of?
What specific energies of that radiation are you speaking of?
What specific dose rates due to those energies and kinds are you speaking of?
Are these doe rate levels static or changing over time and has that been accounted for?
Bingo.
Nope. Radiation isn't that strong in space. The capsule will do the job just fine.