Yes, we've been advised multiple times already. In the utmost emergency we'll do it ourselves. But we are not professionals, nor hobbyists; neither my husband nor I have ever mounted a shelf. My dad (later a craftsman) always did that for me during his lifetime, and my husband grew up without a father, in a country where nobody builds houses out of stone. Both IT specialists. So there is 0.0 experience.
According to your story, I would steer clear of it myself.
Again, various options besides doing it yourself:
a) ebay classifieds/MyHammer together with other small tasks that surely still need to be done for you.
b) Call all local companies/caretaker services, etc., all-round service providers (and offer it together with other tasks)
c) Put the washbasin on a table (simply doable yourself) and stick the runners to the tiled wall in two or three places without drilling, done and dusted.
d) Take a wooden board and go to the nearest sawmill/carpentry and ask them to drill the pre-marked hole and then pay for it.
e) Implement other options mentioned by other forum members.
If none of this leads to success, then I really advise selling the house again, because with a house there are always similar things to deal with that either you yourself or another person has to handle.
But it probably won't come to that, because in my opinion, the problem is not really a real problem. Do it as various people suggested here and the thread will soon be positively closed or send me your place of residence and I guarantee you to find someone who will hang this thing on the wall! Ufff... I just can't believe it right now.