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Yes, That is a pressed fit. I still remember the day I did a power shift from first to secound in the LT-1 and came up with the whole lever in my hand. I was lucky that was all that happend
Mine was quite wobbly there, I tack welded it and the "tacks" lasted all of 5 minutes after I went through the pain of reinstalling it. I gave up and bought a Hurst comp plus...MUCH better unit! Now I have a Tremec, I'll probably be selling the Hurst (might not be the one for you though, '68 was an odd year for everything ).
I see no problem with welding it if you want to stay stock, but I would weld it solidly all the way around.