Your example is perfectly legal. Scrambling is not really a combat move but a defensive move that happens on another player’s turn (in this case it would be UK’s turn). So while both of these actions occur in the same round, they are in different turns – combat move on Germany’s turn, scramble on UK’s turn. The only way you would have to make a choice as to which battle your German fighter participates in is if the UK attacked both SZ97 and Southern Italy. Then you have to decide whether the fighter defends Southern Italy or scrambles to defend SZ97. It can’t do both.
By the way, I assume that you meant the UK attacks Italian ships in SZ97, as that is adjacent to Southern Italy. SZ117 is up in the North Atlantic.