This should be a fairly simple project, except for the major issue:
Obviously the lack of power transformer. Properly rated 1:1 isolation transformer would be suitable except that heater winding is in series with the motor to drop the filament voltage to suitable level. You need to figure out a way to achieve the same without the motor. Regulator circuit or just another transformer for filaments perhaps?
Everything else should pretty much work as is for the task. The selenium rectifier would have to go for reliability reasons and likewise I'd be worried about condition of ALL components in a unit as old as this.
Just my opinion, though: Why? You ruin a perfect vintage record player to get a feature-limited practice amp for guitar. Do you seriously think you will enjoy an amp like that more than through the initial thrill? If I were you I would just wire a phono jack and switch in there and make the input selectable between phono pickup cartridge or the phono jack. There. Done.
Do you really want to waste more time for this concerning the outcome?
Guitar Amp from Old Record Player
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