Breaking it down with the example of playing in F.
The VI chord is Dm (DFA)
The I chord being F (FAC)
By playing the I triad over the VI you’d turn it into a Dm7 chord.
The II chord is Gm (GBbD)
The IV chord is Bb (BbDF)
By playing the IV triad over II you’d turn it into a Gm7 chord.
Therefore this shouldn’t cause an issue as it’s common to incorporate the 7th in a blues and both the original chords are minor.