Fetching details from the dictionary...

to interfere (with); to hinder; to be hindered (from doing); to become impeded; to have difficulty; to suffer inconvenience
体調が悪く業務に差し支えるおそれがある。
My physical condition is poor and there is a risk it will interfere with work.
この情報は公開しても差し支えないと判断した。
I judged that there is no problem with disclosing this information.
少し遅れても差し支えなければ午後に届けます。
If a slight delay is not a problem, I will deliver it in the afternoon.