Well, that depends. Time Signatures imply an inherent beat structure. 4/4 will have 4 beats of 1/4th notes. 9/8 as three beats each made up of 3 1/8th notes or one dotted 1/4th. Depending on what your music actually does this might be exactly what you want, or it might be confusing. Other options might include 4/4+1/8 or even simply 18/16.
About the tempo: Tempo is not given in beats per second, but in a specific duration value per second. Common modern consensus is that this tempo remains the same even if time signature changes happen. This would have been different in baroque time, which is why there is some old practise of putting the tempo indication L’istesso tempo (the same tempo) to indicate that the tempo does not change.
From what you’re saying you seem to imply you do not actually want this, but you want to have this 9/8 measure to be played in half the tempo of the 4/4 measures. This could simply be done by putting eighth = quarter as tempo indication.
But why not simply use one 9/4 with double note values instead? This way you would not induce any confusion by suddenly taking half the tempo for a single measure.