I think that you will get more warmth from a cart or phono stage, rather than from a cable swap. But do not assume that a TT is just like an amp or CD player. The signal level is much much lower. Which makes cables from your cart to phono stage the most important in your system.
That said, look for a warm cart or phono stage. Grado is one place to look on the cart side, available at a number of price points. The EAR phono stages are often described as warm, but that may be outside your budget. Maybe others know less expensive phono stages that meet your criteria.
That said, look for a warm cart or phono stage. Grado is one place to look on the cart side, available at a number of price points. The EAR phono stages are often described as warm, but that may be outside your budget. Maybe others know less expensive phono stages that meet your criteria.