Marriage for executioners in Medieval times

Your only question seems to be whether an executioner would be able to be wedded by a priest?

According to German wikipedia,

Es war bereits sehr schwer für sie, bei der christlichen Taufe Paten zu gewinnen. Dieser „unehrliche“ Beruf hatte allerdings auch weitere Tabus zu befolgen – so war Scharfrichtern beispielsweise ein gesonderter Platz in der Kirche oder auch im Wirtshaus vorgeschrieben.

It was already hard for them to find godfathers for a Christian baptism. This "dishonorable" profession however had to adhere to further taboos - for example they had to use special seats in churches or also in inns.

IMHO this means that executioners could go to church and also have their children baptized. I believe it follows they could also be wedded by a priest.

Some corrobation for the town of Brandenburg here:

Bei der Taufe gab es keinerlei Unterschiede zu anderen Christen, die regelmäßig an Gottesdiensten teilnahmen. [...] Von einer Verweigerung der Taufe aufgrund der „unehrlichen“ Berufsgattung, wie es vorwiegend in der älteren Literatur zu lesen ist, ist in den Kirchenbüchern der Stadt Brandenburg nichts zu finden.

Die wenigen Hinweise aus den Akten des Domstiftsarchivs Brandenburg sowie des Stadtarchivs lassen darauf schließen, dass auch die Heirat in Scharfrichterkreisen durchaus dem christlichen Zeremoniell unterworfen war und hier keine Ausgrenzung erfolgte.

With regard to baptism there was no difference to other Christians who regularly attended church service. [...] About a refusal of baptism due to the "dishonorable" profession as can sometimes be read in (predominantly) older literature there is no trace in the church books of the town of Brandenburg.

The few hints from the documents of the Brandenburg cathedral chapter allow the conclusion that also marriage in executioner circles adhered to Christian ceremonies and that there was no discrimination in this regard.

Some more corrobation re. baptism here, with a number of baptisms of children of executioners in Westphalia in the 17th and 18th centuries mentioned.

This website claims that it was impossible for executioners in a part of Bavaria to marry in church or have their children baptized, but IMHO this website does not look as reliable as the other sources above. But note that there generally were a lot of differences between different regions of Germany, e.g. Bavaria and Westphalia staying catholic and Brandenburg becoming protestant in the 16th century.

Regarding whom executioners or their sons married, the overwhelming consensus seems to be that they usually married daughters of other executioner families. As Heinrich Heine wrote about the situation in the 19th century:

An manchen Orten wird das Glas zerbrochen woraus der Scharfrichter getrunken; niemand spricht mit ihm, jeder vermeidet die geringste Berührung. Diese Schmach ruht auf seiner ganzen Sippschaft, weshalb auch die Scharfrichterfamilien nur unter einander heurathen.

In some places the glass from which an executioner has drunk will be broken, no one talks to him, everyone will avoid the slightest physical contact. This disgrace applies to the whole family, which is why executioner families only marry among themselves.

This is kind of what you would expect if a) executioners have children, and b) those children are outcasts because of their father's profession.

However, it seems that at least one instance of an executioner marrying a convict is actually documented (same source already cited above):

An dieser Stelle soll noch eine Besonderheit scharfrichterlicher Begnadigungsrechte kurz angesprochen werden. Gemeint ist hier die Errettung einer Delinquentin vor dem Tod durch Heirat. So geschehen im Jahre 1525: der zur Aushilfe nach Nürnberg berufene Rothenburger Scharfrichter bot einer Kindsmörderin die Ehe an und rettete sie dadurch vor dem Tode durch Ertränken.4 Derartige Fälle sind aus Brandenburg jedoch nicht bekannt

In this place a special case of the executioner's right to pardon should be mentioned, which is saving a female convict from death by marrying her. This happened in the year of 1525: The Rothenburgian executioner, who at that time was helping out in Nuremberg, offered marriage to a child murderer and in this way saved her from death by drowning. Such cases are not known in the [town of?] Brandenburg, however.

One book with a more in-depth treatment of this topic seems to be "Scharfrichter und Abdecker: Der Alltag zweier "unehrlicher Berufe" in der frühen Neuzeit" by Jutta Nowosadtko.