Don't underestimate the devastation this will cause.
To the other siblings, the other friends and definitely to your mother.
My friend nearly did this- for her it was a visa wedding, in that they wouldn't have married when they did but they had a job offer abroad that required them to be married. She was going to do it a bit like you, two friends who happened to be local as witnesses, but had a wobble and invited parents, siblings, one close friend each and the original two witnesses- 15 people who saw the vows and went to the pub after.
My friend loved the day, and is really glad she invited the people she did- I wasn't allowed being my now-husband, who was friends with her in his own right, so they really did keep the numbers small, which actually meant nobody was offended. Everything was v low key and meaningful.
Despite this, Her mother still hasn't fully recovered from only getting two weeks notice, and was quite upset that it was clear they were going to go ahead without them being there or telling them. I know that even now, years later, she sometimes brings up with my friend that she's worried they did something wrong, or something my friend hasn't told them about, that she would plan to marry without wanting them there.
they kept the witnesses as being the local Ines they'd asked, and definitely didn't have bridesmaids/groomsmen, but the registrar referred to the female witness as the 'bridesmaid' and it did hurt- we were always meant to be each other's bridesmaids, and she was mine a few years later. Ive never mentioned it to her but if you do have friends closer than the ones who will be there, while they may not say anything, they may inwardly feel hurt these friends were included, regardless of circumstance.
I think the issue is: you say you don't want a fuss, but you're potentially setting up years of hurt and resentment among the people you love. We got married for us- legal reasons, and because we loved each other and after years together wanted to start a family. We had a wedding for our families- our priority was basically letting people who love us know that we see them as part of the new family we're forming. Im aware weddings can be a production, but the nicest ones I've been to were small, cheap and didn't buy into any of the usual rubbish- they were celebrations of the couple and a message from them inviting those there into the next chapter of their lives.
Think hard about the message you're sending. It's very difficult to take it back afterwards.