Reddit mentions of Turntable Cartridge Headshell Wires

If it would be less of a hassle to just get a replacement cartridge I would consider it, my budget right now though is only about $50... Thanks for any help r/vinyl! I am excited to get this thing making music :D

edit: would this be a good starting point?

http://www.amazon.com/Shure-M44-7-Standard-Turntable-Cartridge/dp/B00008W2LW/ref=sr_1_11?ie=UTF8&qid=1375480313&sr=8-11&keywords=shure+phono+cartridge

http://www.amazon.com/Turntable-Cartridge-Headshell-Cables-Oxygen/dp/B009W2BE0M/ref=sr_1_31?ie=UTF8&qid=1375480670&sr=8-31&keywords=shure+phono+cartridge

Yeah I was thinking. Do you think I can solder it into one of these? https://www.amazon.com/SPECIALTY-AV-OFCGL2-Turntable-Cartridge-Headshell/dp/B009W2BE0M/ref=sr_1_3?ie=UTF8&qid=1537325023&sr=8-3&keywords=headshell+wires&dpID=311DXYIY9qL&preST=_SX300_QL70_&dpSrc=srch

I tried to change out the cartridges on my Harman Kardon T30C, but the output pins on the cartridge are too large for the headshell leads. What step do I take from here? It originally had a Grado MF 2 cartridge. The new cartridge is an Audio Technica AT 95E. The manual for the T30C says not to use any other headshell than the one provided so changing out the headshell isn't an option I suppose.

Here's a pic of the cartridges to see the difference in size:
http://imgur.com/a/EDFeB

Do I try to change the leads? Or purchase a different cartridge? Would these leads work?

These? https://www.amazon.com/SPECIALTY-AV-OFCGL2-Turntable-Cartridge-Headshell/dp/B009W2BE0M/