I guess the problem is that you can't sign an email, so they can pretend they are not officially bind by your mail. Since they seem to be(from all the crap I read about them) major a-holes, I would comply if I were you.

No matter where you live and who you are dealing with, it is always wise to send any cancellation of a business transaction by registered post.  You need to have written proof that you did indeed send a written communication to that effect.

Make a copy of the signed letter before sending it. 

Keep the receipt. 

Just go to any post office and ask to send your letter as "registered" (anyone knows what that's called in French?)

All that means is that when the letter is delivered to Holmes Place, the postman will ensure that someone at Holmes Place signs with the postman to confirm that your letter was received. 

Hi Nir, its called "lettre Recommandé"

Here is the link of the swiss post about that:

https://www.post.ch/en/business/sending-transporting-mail/domestic-letters/registered-mail?query=lettre+recommande

To make sure that a letter is received before a certan date with proof, a further safeguard is to send it by  'lettre recommandé avec accusé de réception'.

This will cost you 5fr more, but  as well as proof you sent it on a certain date before the deadline, it obliges the recipient to sign for it on delivery, therefore proving they received it on time/on a certain date.

Or just walk over and submit this letter in person keeping a copy signed by Holmes of good receipt? 

Sorry, but I wouldn’t recommend this idea.  An official Post Office receipt of delivery and reception has more authenticity in the event of any future dispute.

I did this with my regie - was closer to walk to them then to go via a post office - they took one copy and gave me the second copy stamped for receipt of it + the date. I think that's even better than a post stamp, no?

Thank you guys il do the "lettre Recommandé".

have a nice weekend

In my view the comparison between the business practices of a régie and a health club can leave much to be desired.