PWM 1Hz on solid state relay
Would it create more wear and heat on the solid state relay, or should I do manual pwm over say 10 seconds?


No. The SSR switches on every mains half-cycle anyway. 

For this type of application a zero-cross SSR is a good idea to reduce mains interference.



Figure 1. Adjusting duty cycle using a zero-cross SSR. Source: LEDnique.

For further reading see my answers to:


Using AC current to trigger Triac explains the internal working of a zero-cross SSR.
Confusion with TRIAC firing and zero crossing point.




Counterfeit Fotek SSRs

It appears that you are considering Fotek SSRs. Read this first: 
UL warns of solid state relay with counterfeit UL Recognition Mark (Release 13PN-52). The one you have pictured is counterfeit. 

See also Big Clive's Teardown of an eBay 25A Solid State Relay (SSR).