Let $f,g \in \mathbb{Q}_p[x]$ be two monic $p$-adic polynomials of the same degree $n$ and write $$f=x^n +a_{n-1}x^{n-1} + \cdots + a_0, \qquad g=x^n+b_{n-1}x^{n-1} + \cdots b_0.$$
Let $K_f, K_g$ denote the corresponding splitting fields. Is there an explicit constant $C$ (depending on $n$ and $p$ probably) such that if $|a_i-b_i|<C$ for all $0 \leqslant i \leqslant n-1$, then $K_f \cong K_g$?
I feel like an ineffective version should be given by Krasner's lemma (although this may assume irreducibility). I'm looking to use it for an explicit numerical example and hence would like a bound - I don't care how sharp it is.