Cleaning injection blood: Is water necessary?

Assalāmu ʿalaykum wa raḥmatullāhi wa barakātuh, I sincerely apologise for the urgency of this message, but I have just realised something that is causing me a great deal of stress and worry. I follow the Ḥanafī madhhab. Every morning when I wake up, I take insulin injections - one in my stomach and another in my buttocks. Often after the injection, some blood emerges and flows away from the site. What I usually do is stop the bleeding with a dry tissue (this typically takes around 5–10 seconds), and then wipe away any blood from the surrounding skin. After doing this, there is no visible blood left at all. Has this been sufficient for ṭahārah, or was it obligatory to wash the area with water after wiping away all the blood? If washing is required, how exactly should I do it? Would wiping with a wet tissue be sufficient, or does the water need to actually flow over the skin? It would be very difficult for me to position my stomach and buttocks under running water each time and ensuring that the water reaches the exact affected areas, especially on a daily basis. I also want to clarify that my question is not about bleeding while in a state of wuḍū’. I was already not in a state of wuḍū’ before the injections anyway. My concern is specifically whether wiping away the blood from the skin is sufficient for purification, or if using water is obligatory. I am very worried that my prayers may not have been valid, as I have been doing this for most of my life. I would be more than happy to explain this over the phone if that would be helpful. Jazākum Allāhu khayran for your time and guidance.