ZS7User - No, the Canon SX10 does not have a thread for filters. What it does have is a 'groove' - which holds the lens-cap on.
(After the flimsy Canon lens-cap fails, get a generic "DSLR lens cap" from a camera shop. I got one better-fitting than the Canon original for AUD$9.00.)
The SX10 does have a bayonet-fitting on the lens barrel for the supplied hood.
The Lensmate folk make a very light but strong adaptor ring - for SX10, SX1, SX20 - that rotates into the hood's bayonet-fitting, instead of the hood. The filters screw into the adaptor's 58mm thread.
Google the Lensmate site to see how it works.
From pictures of the ZS7, it looks as if the lens telescopes back in flush with the camera body - making it slim and easy to pocket. So the filter setup that fixes to the barrel and has the slide-in square or round filters might not work - somebody here might know how to rig a "temporary slide-on" that does.
You might be able to make an elastic "collar" - look at elastic widths at a "home sewing" place - that could have about 3 small clips attached - that'd hold your 1 or more NDs in place for the longer periods needed to get the water-flowing effects. You'd need to be careful and remove it before the lens retracted, though.
With the polariser, you have to be able to rotate it to first find, then adjust, the effects. Screw-in polarisers are "two-piece" - that is, they have a base-part that usually screws into the lens (or adaptor) threads - and a ribbed-edge outer part that rotates freely.
If you take your ZS7 to a camera shop - show the assistant the diameter of the extended lens - and they'd be able to find one that "just-fits" over the end. This would prevent it "slipping around" and make it easier to hold in place and rotate - while looking at the LCD-screen - not at what you're doing with the filter.
Shots with polarisers on P&S cameras won't be "long period" - at most a few seconds. So you could use a tripod to actually hold the camera, hold the polariser in place with your left hand, and adjust the camera with your right.
You probably won't want a full-size tripod when traveling about. So get a "table" sized one that fits in pocket or carry-bag.
Again - don't buy 'the cheapest" - they'll wobble-about (been-there, done-that, too...!) - get one that's solid and firm - I paid $25.00 for one - after a "$10.00 wobbly".
Just use it as an "aimable support" - don't extend the legs, so it will be at its steadiest - just place it on a handy object.
Google GorillaPods - while they cost a bit more than table tripods, they attach to many objects firmly - so might do as you need.
If you can mount the camera firmly in one of those ways - and others might have better ideas, too - you could set the shot up with the polariser at the desired-effects rotation angle - set the camera timer so the camera doesn't "vibe" from the shutter-pressing at the actual-shot time - and as the timer runs - 2-seconds might be enough - gently hold the polariser in position.
Sorry - the cruddy-cheap filters went in-the-bin - and the messes-pix they made have long been deleted.
Here's one done by the Hoya Std CIR-PL polariser with the Lensmate adaptor on the Canon SX10. Distance was about 60ft - so this is a crop. (At 20x / 560mm equiv.) Aperture Priority, f/5.6, 1/250th and ISO-80.