Slicers will perform a retraction when moving from one solid to another, the value of which is part of the settings. I've not researched if a specific slicer will allow a negative retraction, but if it's possible, it's likely to create adjustable stringing.
If negative retraction is not possible, one can identify the retraction segments in g-code of the print and find/replace those values with extrude rather than retract. My slicer, Simplify3D does not support reversed retraction, but the code is clear when examined with a text editor:
G1 E-4.0000 F2400
G1 Z0.300 F1200
G1 X118.760 Y117.415 F12000
G1 Z0.250 F1200
G1 E0.0000 F2400
G92 E0.0000
G1 X122.415 Y113.760 E0.0972 F900
build g-code removed for clarity
G1 X118.760 Y117.415 E1.5303
G92 E0.0000
G1 E-4.0000 F2400
G1 Z0.300 F1200
G1 X158.280 Y117.216 F12000
G1 Z0.250 F1200
G1 E0.0000 F2400
G92 E0.0000
G1 X162.216 Y113.280 E0.1047 F900
build g-code removed for clarity
G1 X158.280 Y117.216 E1.5902
G92 E0.0000
G1 E-4.0000 F2400
build g-code removed for clarity
G1 E0.0000 F2400
G92 E0.0000
G1 X162.415 Y113.760 E0.0972 F900
build g-code removed for clarity
G1 X158.760 Y117.415 E1.5303
G92 E0.0000
G1 E-4.0000 F2400
All entries beginning with G1 E-4.0000 represent the 4 mm retraction called by the slicer. One could search for just that code and replace it with a positive value. Some experimentation is indicated to accomplish the desired result. The F value is feed rate and presents another value to adjust.
Pursuant to Oscar's comment, I overlooked the lack of movement as a factor. He is correct, such a modification is likely to create a blob. As a possible compensation, a better modification would be to create a custom extrusion code with a reduced flow rate, using the existing code as a reference.
This starts to complicate the process substantially, requiring far more calculations and edits. I suggest that it could yet be accomplished, but would be more easily done so with post processing of the code via Python or similar, with which I am not qualified to address.