Multiple VLANs But Can't Use Trunk

Hey All,

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Have a quick question. If I have the need to pass traffic for multiple VLANs from a switch to a router but am not able to have a trunk link between the two, am I then able to connect multiple cables between the two as access ports on either side.

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From what I understand the access ports on the switch that are closest to the computers will tag that traffic entering ingress on those ports with the VLAN number. The access ports on the switch closest to the router will strip the tag when traffic leaves egress on those ports and will traverse the link untagged, and then will get tagged again when they access my router's access ports, correct?

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So an example traffic flow:

VLAN10 Computer sends a DHCPDiscover > Enters Access VLAN10 on Switch > Leaves Access VLAN10 on Switch closest to router and gets untagged > Enters Access VLAN10 on Router > Routers responds back in the reverse patch with DHCPOffer

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Here is a diagram that may explain better than I can:

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https://i.imgur.com/KrlNgG6.png

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Don't ask why I can't use a trunk instead of 4 cables, it's a long story....