I am not aware how you would disable a type of contract when starting the game in unmodded KSP, however the default contract system is dynamic, and adjusts based on what contracts you accept and ignore.
Each contract type (and each celestial body) has a weight, and that weight determines the chance of it appearing. Accepting contracts increases the weight of that type of contracts, ignoring or declining contracts reduces their weight.
So if you keep ignoring or declining the part contracts, you'll start seeing less of them. Declining gets rid of them faster than ignoring, but costs a bit of reputation.
The specific weight constants are located in the Contracts.cfg file, as of KSP 1.2.1 they are:
- WeightDefault = 30 // The default weight new contract types start with
- WeightMinimum = 10 // The minimum weight that contracts can have from declining them
- WeightMaximum = 90 // The maximum weight that contracts can have from accepting them
- WeightAcceptDelta = 12 // How much accepting contracts affects their weight
- WeightDeclineDelta = -8 // How much declining contracts affects their weight
- WeightWithdrawReadDelta = -2 // How much an expired contract that was read affects their weight
- WeightWithdrawSeenDelta = -1 // How much an expired contract that was seen (showed up in mission control) affects their weight
Now, if you really want to get rid of all the part contracts right away, you can go into your Kerbal Space Program/saves/<savegame_name> folder, open up the persistent.sfs file with your favorite text editor, find the part which says WEIGHTS, and edit those weights to whatever suits your fancy. In your case, you would want the PartTest variable in the WEIGHTS section.
From my brief testing, setting the weight to zero seems to disable the generation of that type of contracts completely.