Edit
I just read your question properly - I do not believe there is a way to use a non-RColorBrewer palette with the process_map() function. A potential workaround is to find the source code and create your own function based on the bupaR function to accept other palettes, but as far as I can tell it will only accept RColorBrewer or Viridis palettes at present.
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Depending on your use case you could use colorRampPalette() to build your palette from white to #004b88, e.g.
To see "Purples":
library(RColorBrewer)
scales::show_col(brewer.pal(6, name = "Purples"))

To create and see a new palette:
palette_blues <- colorRampPalette(colors = c("white", "#004b88"))(6)
scales::show_col(palette_blues)

And if you want more than 6 colours or you don't want to start with white you can change the number and 'drop' some from the end, e.g.
palette_blues <- colorRampPalette(colors = c("white", "#004b88"))(12)
scales::show_col(palette_blues[4:12])

What is the best color palette to use in R?
Which R color palettes are colorblind-safe?
How do I get more colors than a palette provides?
I often do the following,
library(RColorBrewer)
my_palette = c(brewer.pal(5, "Set1")[c(1,3,4,5)], brewer.pal(5, "Pastel1")[c(2,5,1,3)])
#grid::grid.raster(my_palette, int=F)
scale_colour_discrete = function(...) scale_colour_manual(..., values = palette())
dsamp <- diamonds[sample(nrow(diamonds), 1000), ]
(p <- qplot(carat, price, data = dsamp, colour = clarity)) # default palette
palette(my_palette)
p # custom colors
A simple solution without creating an additional function is to use the HEX code. If you use the RcolorBrewer website, each palette colour has one. Example:
scale_color_manual(values=c("#1f78b4","#a6cee3","#fc8d62","#e41a1c"))
With the codes in the order that you need them in accordance with your other ggplot2 layers. This way, you can cherry-pick and combine colors from different RcolorBrewer palettes.