I came up with 'si cela ne vous dérange pas mon demandant' but Google Translate is saying it's 'si cela ne vous dérange pas de demander'. Could someone help
In the phrase "my asking", the word "asking" is grammatically a gerund:
The gerund is a verb which is used as if it were a noun ... [for example] "Seeing is believing"
It's formed from the present participle of the verb.
French verbs have a present participle (e.g. manger / mangeant) but I think they're not used as gerunds i.e. as nouns. You could never say bon mangeant in French like you might say "good eating" in American English.
Instead I think the French tend to use the infinitive form of the verb, e.g. bon à manger ("good for to eat" also known as "good food"), or voir c'est croire.
So mon demandant is no good. If you want to use a noun in the phrase, you say ma question.
Also I think that asking, "If you don't mind..." is slightly rude: perhaps it's imposing on you to decide.
So a slightly politer English version (which doesn't ask you to commit yourself before you've even heard my request) might be to ask, "If I may, ...".
That's where other answers are suggesting Si je peux or Si je puis.
Also, the distinction in English between "If I may" and "If I can" is, in French, the difference between pouvoir and permettre.
Again, I think it's more polite to say "If I may permit myself to..." than "If you will permit me to..." -- I think you're expected to be well-behaved, to govern your own behaviour, to know what's right and wrong, and to not impose that responsibility on others.
That's where another answer suggests Si je peux me permettre instead of Si vous me le permettez.
Sometimes if you get a cold-call, i.e. a business phone call from someone you don't know, they'll explain the reason (i.e. why they're allowing themselves to call you) by starting, Je me permets de vous contacter parce que...