When calculating the distance between molecules in a solution, is it reasonable to approximate a sphere around each molecule?
The distribution of molecules in solution is not uniform but has a distribution. The calculation of nearest neighbour distances from one molecule to another has been worked out a long time ago see,  S. Chandrasekhar, Rev. Mod. Phys. 1943, v15, p1.
Let $w(r)$ be the probability that the nearest neighbour occurs between distance  $r$ and $r+dr$. This must be the probability than no molecules exist closer to the victim molecule that one occurs at a distance $r$ and that this molecule exists in the shell $r$ to $r+dr$. Thus,
$$ w(r)=\left(  1-\int_0^r w(r)dr \right)4\pi r^2 n$$
where $n$ is the average number of molecules / unit volume. (1 mol/m3 $\equiv 10^3N_A/10^{27} = 0.6023 $ molecules / nm$^3$).
This looks hard to solve because $w(r)$ is also inside the integration, so it is necessary to isolate the integral first (by dividing both sides by $4\pi r^2 n$) and then differentiating both sides to find
$$\displaystyle \frac{d}{dr}\left(\frac{w(r)}{4\pi r^2 n}\right)= \frac{d}{dr}\left(1-\int w(r)\right) =-4\pi r^2 n \frac{w(r)}{4\pi r^2 n}$$
and the last step we effectively multiply by 1. The result is
$$ w(r)=4\pi r^2n\exp(-4\pi r^3n/3)$$
The average distance between molecules is
$$\langle r \rangle =\int_0^\infty rw(r)dr =\Gamma (4/3)/(4\pi n/3)^{1/3} =0.55396n^{-1/3}$$
where $n$ is in number of molecules/volume then $n^{-1/3}$ is in units of length.