I have not made my mind up on it yet, one week was just an example of a duration that hasn't been discussed in previous threads. I just realized I had not worded the question I had wanted to ask all along: Is there any way a short trip can be interpreted negatively and harm the application? (in the way that proposed trips being too long can indicate weak ties and potential to overstay)
Several applicants apply for short visits or one week or even less..... business visitors.... someone visiting for an exam/interview/conference.... or even tourists/family visitors who are visiting the US and want to see the Niagara Falls from the Canadian side (for example).
On the contrary, a short 1-week visit may not work for some applicants.... first-time travelers abroad and/or someone who doesn't have adequate financial resources, etc
I suggest you first apply for a visitor visa to either the UK or a Schengen country (pick a country which is perceived as being more generous in issuing visitor visas to Indian passport holders). This would help you to understand how to prepare a visa application + that visa could add to your travel history/visa history/may help for your TRV application later.
TRVs are not easy to obtain. IMO, you are risking a refusal given your personal/professional circumstances. In the end, being super precautious/trying to base your application on what worked for someone else, may not help your case.
The fact you are unable to explain why you want to visit and/or you are ultra-flexible for the duration of your visit seems to indicate you are not a genuine, short-term visitor