No. This is not allowed. This is a classical example of Talfeeq Batil i.e. mixing various rulings to come up with a new action that is not endorsed or held by anybody. This is Talfeeq Batil, because all the scholars who said that bleeding doesn't break Wudu say that it does break when a man touches a woman, and all scholars who say touching a woman doesn't break Wudu say that it does break when one bleeds. This is not allowed by scholars.
This is because when you start mixing rulings of different madh-habs, you start following your nafs and fancies. We believe all madh-hab rulings are valid since they are based on evidences from Qur'an and Sunnah. But, the madh-habs have some major differences in some opinions. And when you start to mix opinions, you end up following your nafs which not really based on Qur'an and Sunnah, you make yourself the authority. It is not permissible for someone to follow a opinion or switch them or mix them based on convenience. And also, all madh-habs make talfeeq baatil impermissible.
However, note that there is permissible form of talfeeq and impermissible form. The example you have given comes under impermissible. A impermissible talfeeq is what is based on desires and conveniences.
Basically you cannot "pick and choose" whatever you like. At the same time, I am not asking someone to adhere to a madh-hab 100% [this is just for caution]
Summarizing Prohibition of Devising Opinions and Following Allowances:
Majority of the latter scholars in Maliki, Shafi'i and Hanbali prohibit Talfeeq absolutely while, most of the Hanafis allow it.
The impermissible form of talfeeq is where the end result in and of itself is Haraam, such as the consumption of alcohol or fornication.
Another impermissible form of talfeeq is to hunt out most lenient opinions of madh-habs and scholars.
The one who seeks such opinions is considered faasiq (someone who violates Islamic law(s)) as stated by Ahmad and also an opinion of among Shafi'is. Ibn ‘Abdil-Bar also mentioned consensus (Ijma’) on this issue.
Source: excerpts from student of knowledge Harris Hammam