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LingakuLingaku[verb て-form] + も差し支えない [i-adj 〜い → 〜くて] + も差し支えない [na-adj] + でも差し支えない [noun] + でも差し支えない
ても差し支えない is the formal way to say something is allowed or causes no problem: "it is no problem if ~", "you may ~". It follows a verb's て-form, and a noun or な-adjective takes でも差し支えない. さしつかえ差し支え means "hindrance", so the whole is literally "even if ~, there is no hindrance".
It belongs to business, official notices and careful requests. In everyday speech the same thing is てもいい, or a step up, てもかまわない構わない. Said politely it becomes さしつかえ差し支えありません, and to a customer さしつかえ差し支えございません.
As a question it asks very courteously, with でしょうか or ありませんか on the end.
Without ても, さしつかえなければ差し支えなければ is a fixed opener for a request: "if you don't mind".