Palal, RussellJ and IAN-UK already gave great advice. I agree with all and won't repeat here.
You mentioned kayaking. There is a non-profit water sports club based in downtown Cascais, with their kayaks based right there at Praia dos Pescadores (the most downtown beach, in front of city hall and
Hotel Baia and adjacent to the
Naval Club). Not at all like the commercial outfits you will see renting kayaks, most based out of Guincho beach for €50 and up and Summer only. I have rented kayaks from these guys for €5-€10 for a couple of hours. They are
ADN Cascais, and won't come up in any reasonable Google search because they are not geared towards tourists. It's really a local club, but they are super friendly and real water sports enthusiasts. The trick will be getting them excited enough about serving you in November. If you're serious about kayaking, reach out to ADN during Summer and perhaps you will strike a relationship with someone who will be willing to help you out in November. As for kayaking, the bay is quite well protected with beaches and coves to explore, but as soon as you turn the breakwater you're in open Atlantic waters and it can be a difficult and wild ride, especially in November. Be extra careful, as winds and currents can be pulling you out sea or onto rocky cliffs. You'd better be a good experienced ocean kayaker and in very good physical shape. And you may want to get one of the experienced local guys to go with you, they know the currents and where not to go.
You also mentioned hiking. There are some superb hiking opportunities in the mountain between Cascais and Sintra. Without your own transportation it will take planning to get to the trailhead, and even more planning to get picked up for the return. You may want to rent bikes, and the Cascais municipality has an excellent bike rental service "BiCas". You can't reserve them, they're first come first served, but in November there will be little to no demand. You could use a bike to get to the trailhead. You could also use a taxi to get to a trailhead, but getting one to come back is a challenge. You could also rent a car, and in November in Cascais you should be able to get them for less than €10/day.