I have a regular walk-behind mower that has the "automatic" speed-control thing on the handle––it only runs one speed.

I want to put a manual-control throttle onto it, so I can run it at a lower-than-normal speed (to use a thatching blade).

I've seen replacement cable throttles various places, but I've played with the mower's throttle linkage before and there's no immediate way to just hook a manual throttle onto anything there that would work. The carb has a little linkage that runs up into the cylinder head area that moves maybe a eighth-inch total, and that causes the engine to run from ~5000 RPM to "off".

Does anyplace sell a kit for doing this? The mower is a Craftsman 4.5hp horizontal single, there was no name-badge on the engine itself.
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Do you mean to eliminate the governor? I would guess any lawnmower shop would have what you need.

From your description you have either a 21 or 22 cut front wheel drive. If so, the drive system is belt driven to a single speed transmission. Depending on the specific model to move the transmission from neutral to engage it either adds belt tension or has constant tension and a fork inside the transmission engages the gears. On either one, you need to find a way to have the belt "slip" to slow the ground speed. If successful, you may need a new belt to go back to normal speed is the slippage causes the belt to heat up and either glaze over or break.

As far as the engine speed, there is a rpm power and cooling band the engine needs to stay in to sufficiently cool and lube engine. That  band is usually between 3000 and 3600 rpm's.

Craftsman primary engine for walk and self propelled were Tecumseh, but they have been known to use Briggs and Honda. Go to www.sears.com and you will see a place to look up parts by typing in model number. The number will usually start 917.xxxxxx  since AYP has been the primary vendor for many years. It may start, 502.xxxxxx, 536.xxxxxx or a different 3 digit prefix if they used a different vendor.

As far as the cable, just get a universal throttle cable Rotary # 6658 and a throttle plate cable clamp Rotary # 249 or #250.

The fellow above sounds like he knows his shit.

Thanks for the kind words.

BTW you wasted post 757 on it.