Overkill, yes - but if you have it give it a go.10gbe Switch with a Modem that supports those speeds.
Be careful though, some 10GbE switches do not support 100Mbps links, especially if they are SFP+/SFP28 based - and pretty much everything controller wise has 100Mbps interfaces.
You wont need more than a 100Mbps switch; although gigabit may be required if you go to Colorlight cards that only have Gig PHY's on them.
No you dont If you did, you couldnt plug them into regular ethernet hardware which takes 8P8C connectors.I've got CAT7 cables
You've got something (who knows what) which is incorrectly being branded as CAT7.
CAT7 was an interim specification (before CAT6A was released), which uses TERA connectors (left, shown with 8p8c for comparison) - or GG45 connectors (right):