I inquired about this recently. I'm not sure about the advice here regarding "contact your employer for clarification about conflict of interest". You're giving them an extremely easy way to just say "no". It all sounds a bit knee-jerky "be safe".
In the company I work many people have started companies exactly within our discipline, however you follow some simple rules to make sure your free time does not create any problems:
1) 100% complete separation between your current job and your own company. This should be extreme enough to not check+respond to emails during your working hours at your company. If they can prove (with someone for example emailing you an innocent question, which you respond to while on the toilet) you are working while operating your own business, you will cause problems for yourself. You're at one job, work one job. Leave the office, do what you like.
2) 100% complete separation between resources. Where I work, if you use company equipment to work on your own work/hobbies, it de facto applies to the company I work for. That means if I am on my work laptop at home, and I'm just doodling around and prototyping some thoughts using software on that laptop, my employer owns that work. If I purchase a separate laptop for myself, then all good.
3) 100% complete separation between contacts/connections. No, it's not OK on a (day job) business lunch to mention in passing you're working on product A to a distributor of A, and "only signing the papers after hours". Split it up. You begin to live two professional worlds, one at the day job, one at the GmbH.
You will require a Swiss resident to sign the papers starting the GmbH, but you can use various services for that if you want to pay, or ask a Swiss friend nicely. https://secure.startups.ch/ is an example of a service (first google hit, I'm not endorsing anyone).
You can create a plethora of problems by asking for permission first, however you can create problems by going ahead as well. If you ask for permission and there is any perceived difference in the output of your job, your employer may get snarky and say "well hey, it seems like your two jobs are causing an impact". Employers are people, and subject to all the benefits and faults of human beings.
Review your work contract. If in doubt, ask legal counsel to review the contract. You do *not* have to run everything by your company (unless in the sad case you signed a contract stating so). They don't own your life in all work contracts I've seen.
Good luck, start the business, have fun.