I pray that you are in the best of health and faith, insha’Allah.
No, dabbing and clearing away such blood is not considered “flow” and would not affect the ruling.
According to the Hanafi school, blood which flows (beyond the point of exit)  actually or  effectively (such that it would have flowed had it not been wiped/absorbed away) invalidates the ablution (wudu). [Shurunbulali, Maraqi al-Falah; `Ala al-Din `Abidin, al-Hadiyya al-`Ala’iyya]
And Allah alone gives success.