Radiation in space and its effects on chemical reactions?
It depends....

First let's define the "problem space". 

Chemical reactions are typically driven by a few eV (electron volts). "Ionizing radiation" can be keV or MeV which is vastly excessive. In fact that amount of energy is so massive that it would "rip up" the chemical bonding in any material. Only solid metals would be somewhat stable since the 3D lattice locks the atoms into place. $\ce{NaCl}$ for example could decompose to Na metal and $\ce{Cl_2}$ gas. 

Any sort of chemical reaction in space has to have a container of some sort which would mitigate the penetration of the ionizing radiation somewhat. But it surely won't stop all of the ionizing radiation. There are nuclear experiments that are conducted a mile underground to try to remove cosmic particles. 

The primary source of ionizing radiation in our solar system is the sun. So more distance from the sun is your friend. 

"Performing chemical reactions in space" sort of implies that a human is doing the reactions. A biological entity is going to be more effected than any vat of chemicals. So in an environment which humans or plants could safely operate, then performing chemical reactions won't be a problem.