6 days isn't an ideal travel duration for the Pass. The best Swiss Travel Pass for you would be a 4 day pass (which you would use on days 1-4), you would then need to buy a cheaper Saver ticket for Lucerne to Lugano (or use the expensive 1st cl. Gotthard Panorama Express) on day 5. Lugano into Italy is cheap. 4-day pass costs 281 CHF adult, 240 CHF youth <26.
But you only get 50% off Schilthorn (new 2020 rule) and Pilatus so after some quick math (slow morning at work!) I think the Half Fare Card works out quite cheaper for adults / slightly cheaper for youth.
The Swiss Half Fare Card is a 120 CHF card that gives you 50% off basically every trip in a month, including urban transport, and excluding some mountain railways (notably Jungfraujoch, only 25% off if I remember correctly) - but Schilthorn & Pilatus get that discount. Unfortunately, if you use Half Fare Card no discounts apply for youth after their 16th birthday. Still, including the cost of the card and the Schilthorn and Pilatus excursions, total travel costs would be approx 315 CHF so it works out quite well!
Downside of the Half Fare Card is that you still need to buy tickets, whereas with the Pass, except for cable cars you just hop on. And any impromptu excursion will cost extra.
Bottom line: if you value flexibility during the days of vaildity, go for the pass. If you aim for lowest cost, go for the Half Fare Card.