The following is from:
"The two bits to be avoided unless you are absolutely certain you know what you are doing are bit7, the RSTDISBL (external reset disable) bit and bit 5, the SPIEN (Serial Peripheral Interface Enable) bit. Disabling either one is often the cause for "bricked" Atmel µCs; "leave them alone" is good advice."
According to the article SUT0 and SUT1 are clock start up time related bits. It doesn't seem as though it is necessary to use anything special to change them.
You will find the information at the website very usefu. I know I have.
The High Voltage (other names too) programmer you have mentioned should not be necessary if you only changed the SUT0 and SUT1 fuses.
HOWEVER, if you did change the SPIEN or RSTDISBL fuses, you should either get one of the special programmers or just purchase another 328P microprocessor.
If you search the internet for "AVR High Voltage programmer" you will find many ideas for how to build one.
This link :https://electronics.stackexchange.com/questions/33/arduino-as-avr-programmer/71
provides good information.